JP3394467B2 - How to create a Latin rectangle - Google Patents

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a conversion table used for cryptographic communication, an experimental design method, a method for creating a Latin cube used for setting combinations having no identity in statistics, etc. is there.

[0002]

2. Description of the Prior Art For the purpose of explaining the present invention, the basic properties of the Latin cube will be explained. A set of n symbols A = {a
_{Using each element of 1} , ..., a _n } n times, a total of n ³
Pieces in three directions (X-axis (vertical) direction, Y-axis (horizontal) direction, Z
Arrange in a cube with n elements each in the axis (depth) direction, and each element of A appears once in each direction, that is, an nth-order Latin square that does not have the same value at the same position as each other. A superposition of n pieces is called a Latin cube on A or an nth-order Latin cube.

When a first-order Latin cube is A = {0} a (0,0,0) = 0, the two-dimensional display is as shown in FIG.
The display in dimensional coordinates is as shown in FIG.

Next, the basic form of a quadratic Latin cube will be shown. A = {0,1} a (0,0,0) = 0, a (0,1,0) = 1 a (1,0,0) = 1, a (1,1,0) = 0 a (0,0,1) = 1, a (0,1,1) = 0 a (1,0,1) = 0, and a (1,1,1) = 1 As shown in FIG. 3, when these two tables (Z = 0 and Z = 1) are overlapped and displayed in three-dimensional coordinates, it becomes as shown in FIG.

FIG. 5 shows an example of a standard form of a cubic Latin cube in two dimensions. The value of the element (.) In FIG. 5 is an arbitrary value forming a Latin cube. It is set, and the Latin box in this Figure 5 is
The values of the array elements arranged along the X axis, the Y axis, and the Z axis are all in the ascending order (natural permutation) of 0 to 2, and are therefore standard forms (irreducible forms).

Although the number of standard Latin cuboids is not publicly disclosed, when expressed as L3 (n), the total number of n-th order Latin cuboids is n!・ (N-1)!・ (N-1)!・ L3
The value of L3 (n) can be represented by (n), and when n is 5 or less, L3 (1) = 1 L3 (2) = 1 L3 (3) = 1 L3 (4) = 64 L3 ( 5) = 40246, the total number of Latin cubes in each degree is 1st order = 1, 2
Next = 2, third = 24, fourth = 55296, fifth = 278
1803520.

[0007]

The Latin cube has the above-mentioned structure. However, conventionally, there is no method for regularly preparing the Latin cube, and the Latin cube is prepared by trial and error. In the case of creating a quartic Latin cube, for example, if A = {0,1,2,3}, then 0,1,2,3 is the value of the first array element on the X axis, For the second and subsequent rows, the Latin cube was created by shifting the values of the first array element one by one as the values of the array elements in the Y-axis and Z-axis directions. Not only is it difficult and troublesome to create, but the number of Latin cubes that can be created is limited, so it is not possible to narrow the range of use of the Latin cubes and increase the utility value and utilization effect of the Latin cubes. There was a problem called.

Therefore, the present invention was devised to solve the above-mentioned problems in the prior art, and makes it possible to regularly create a Latin cube of a desired degree according to a certain method. It is a technical issue to broaden the range of use of Latin cubes and to dramatically increase the utility value and utilization effect of Latin cubes.

[0009]

Means for Solving the Problems (Hereinafter, refer to FIG. 6) Among the inventions for solving the above-mentioned technical problems, the means of the invention described in claim 1 is a three-dimensional Latin square (longitudinal direction is the X axis, The degree n of the Latin cube R to be created with the horizontal direction being the Y axis and the depth direction being the Z axis is set, and the symbol m for this degree n is permuted and the selection order according to this permutation is set. Has a control unit 1 for setting and setting, and a Latin cube creating unit 2 for setting each position A _IJK of the Latin cube storage array 12 corresponding to the degree n set in the control unit 1. When the box creation unit 2 selects one of the symbols m as an array element E _IJK for each position A _IJK of the Latin box storage array 12 according to a control program predetermined by the control unit 1, this selection decision is made. Along the X-axis I or Y-axis J or Z-axis K Performs in order until the last position A _IJK axis I and Y axis J and Z axes K, each position A
_For each _IJK , select the symbol m in the order of selection so that it is not the same symbol m as the previously determined array element E _IJK of the position A _IJK before the same X-axis I and Y-axis J and Z-axis K, It is in.

According to the first aspect of the present invention, the degree n of the Latin cube R to be created is set and the symbol m corresponding to the degree n is set.
Set permutation and selection order according to permutation,
The permutation of the symbol m and the selection order according to the permutation are, for example, when the order n is quartic and (0, 1, 2, 3) is set as the symbol m, 0 → 1 → 2 → 3 is permuted (natural Permutation), and to select in the order of 0 → 1 → 2 → 3.

The symbol m to be set is not particularly limited, and in addition to the above example, for example, (1, 2, 3, 4)
(A, b, c, d) can be arbitrarily set, and examples of the Latin squares that compose the Latin cube R created according to these symbols m are as shown in FIGS. 8, 9, and 10. Will be things.

Using the Latin cube storage array 12 of the Latin cube creation unit 2, one selection decision of the symbol m as the array element E _IJK for each position A _IJK of the Latin cube R is performed.
From the initial position A ₁₁₁ , as shown in FIG. 11, along the X-axis I, or as shown in FIG. 12, along the Y-axis J, or as shown in FIG. 13, the Z-axis K. but are intended to be performed in accordance with any one of the techniques or carried along, during the selection decision symbols m, previous position a _IJK the same X-axis I and Y axis J and Z axes K and its position a _IJK ,
That is, the position A where the array element E _IJK has already been determined
_Since the value of the symbol m different from the array element E _{IJK of IJK} is selected, by repeating this, the creation of the Latin cube R is achieved.

[0013] That is, one selection decision symbol m as array element E _IJK for each position A _IJK of Latin body R is in the case of FIG. 11, position location A ₁₁₁ → A ₂₁₁ → A ₃₁₁
→ A ₄₁₁ → A ₁₁₂ → A ₂₁₂ → ・ ・ ・ → A ₃₄₄ → A ₄₄₄ , and in the case of FIG. 12, position position A ₁₁₁ → A ₁₂₁ → A
₁₃₁ → A ₁₄₁ → A ₂₁₁ → A ₂₂₁ → ・ ・ ・ → A ₄₃₄ → A
_It becomes ₄₄₄ , and in the case of FIG. 13, the position position A ₁₁₁ → A ₁₁₂
→ A ₁₁₃ → A ₁₁₄ → A ₁₂₁ → A ₁₂₂ → ・ ・ ・ → A ₄₄₃ →
It becomes A ₄₄₄ .

According to a second aspect of the present invention, in the structure of the first aspect of the invention, the position A _IJK before the same X-axis I, Y-axis J and Z-axis K is already determined for each position A _IJK. When the symbols m are sequentially selected so that the same symbol m as that of the array element E _IJK is not selected, if there is no symbol m that can be selected and determined by the arbitrary position A _IJK , the arbitrary position A is selected.
The symbol m of the already determined array element E _IJK of the position A _{IJK immediately} before _IJK is replaced with a selectable symbol m having a lower rank than this symbol m, and the selection decision is continued. It is a thing.

According to the second aspect of the present invention, a method for continuing the selection and determination process of the symbol m when a situation occurs in which there is no symbol m that can be selectively determined at the position A _IJK on the way is shown. In this case, the previous position A _IJK
Returning to, by previously changing the symbol m which is determined in the symbol m of the lower selection order as array elements E _IJK in this position A _IJK, the next position A _IJK symbol m was not capable of selecting and determining Thus, it is possible to obtain the possibility that at least the symbol m _exchanged at the previous position A _IJK can be selectively determined.

According to a third aspect of the present invention, in addition to the configuration of the first aspect of the invention, the selection order of the symbols m is set in the order of the permutation of the symbols m.

According to the third aspect of the present invention, the selection order of the symbols m is specified in the order of the permutations of the symbols m, that is, the natural permutations, and the created Latin cube R is the standard Latin box. Become a body.

According to a fourth aspect of the present invention, the arrangement element E _IJK of the position A _IJK of the first X-axis I, the first Y-axis J and the first Z-axis K is _{added to} the configuration of the invention of the first aspect. The symbol m of is preset to the same value as the standard Latin _cube , and the symbols m of the array elements E _IJK of the remaining positions A _IJK are selected and determined in order from the position A _{122, the} position A _212, or the position A _221. Is added.

According to the fourth aspect of the present invention, the standard Latin cube is simply created. As shown in FIGS. 14, 15 and 16, the symbol m of the array element E _IJK is The position A _{IJK that} is selected and determined remains unchanged along the X axis I, the Y axis J, or the Z axis K.

[0020] That is, one selection decision symbol m as array element E _IJK for each position A _IJK of Latin body R is in the case of FIG. 14, the position _{A 212 → A 321 → A 421} → A
₂₁₃ → A ₃₁₃ → ・ ・ ・ ・ ・ ・ → A ₃₄₄ → A ₄₄₄
In case of 5, position A ₁₂₂ → A ₁₃₂ → A ₁₄₂ → A ₁₂₃ → A
₁₃₃ → ・ ・ ・ → A ₄₃₄ → A ₄₄₄ , and in the case of FIG. 16, position A ₁₂₂ → A ₁₂₃ → A ₁₂₄ → A ₁₃₂ → A ₁₃₃ → ・
・ →→ A ₄₄₃ → A ₄₄₄

A fifth aspect of the present invention shows another configuration of the present invention, wherein the means is a three-dimensional Latin square (longitudinal direction is X axis, lateral direction is Y axis, and depth direction is Z axis). And a control unit 1 for setting the order n of the Latin cube R to be created and deciding the order m and the symbols m corresponding to the order n and the selection order according to the permutation, and the control unit 1. A Latin cube creation unit 2 that sets each position A _IJK of the Latin cube storage array 12 corresponding to the degree n set to 1; setting the order n to the control unit 1; The setting of the permutation and the selection order according to this permutation is achieved by the setting of the existing Latin cube for the Latin cube storage array 12, and the Latin cube storage array is set according to a control program predetermined in the control unit 1. 12 X-axis I and Y-axis J and Z-axis K maximum From the subsequent position A _nnn, back to the position A _IJK along the X-axis I, the Y-axis J, and the Z-axis K, to the position A _IJK at which the symbol m having a lower selection order than the symbol m of the existing array element E _IJK can be selected. That is, from this position A _IJK to the X-axis I
Or the final position A along the Y axis J or the Z axis K
Up to _nnn , the array element E is sequentially arranged so as not to have the same symbol m as the already determined array element E _IJK of the position A _IJK before the same X axis I, Y axis J, and Z axis K for each position A _IJK. Select and determine the symbol m of _IJK .

According to the fifth aspect of the present invention, a method for creating another Latin cube R having the same degree n and the same symbol m as one existing Latin cube from one existing Latin cube is used. It is disclosed, and by using the created Latin cube R as an existing Latin cube, by repeating the same operation, it is possible to create all the Latin cubes R whose degree is n and whose symbol is m.

According to a sixth aspect of the invention, in addition to the configuration of the fifth aspect of the invention, the last of the X axis I, the Y axis J and the Z axis K of the Latin cube storage array 12 in which the existing Latin cube is set. from position a _nnn, X axis I, along the Y axis J and Z axes K, returns to the position a _IJK selection order than symbol m of existing array element E _IJK can select a symbol m is lower, this position a selection decision symbol m array element E _IJK to the last position a _nnn from _IJK, Latin rectangular parallelepiped first X axis I and the first of the memory array 12 of the Y-axis J and then the first Z perform other positions a _IJK except positions a _IJK along the axis K as the target, it is obtained by adding the.

According to the sixth aspect of the present invention, the position A _IJK along the first X-axis I, the first Y-axis J, and the first Z-axis K is selected from the existing Latin cube. A group of Latin _cubes R having the same symbol m as the array element E _IJK can be created.

According to a seventh aspect of the invention, in addition to the structure of the sixth aspect, the existing Latin cube set in the Latin cube storage array 12 is a standard Latin cube. It is a thing.

According to the seventh aspect of the present invention, the group of Latin cubes R formed from the existing Latin cubes is specified as the standard Latin cube.

[0027]

BEST MODE FOR CARRYING OUT THE INVENTION Embodiments of the present invention will be described below with reference to FIGS. In the following description, for convenience of explanation, the order n is 4, the symbol m is a natural number (0, 1, 2, 3), and the permutation and selection order are as per natural permutation.

FIG. 6 shows an electric circuit block configuration of a computer configured to carry out the method of the present invention, where 1 is an order n, a symbol m, a permutation of symbols m and a selection order, and first an array element. position a _IJK selecting determine the value of E _IJK, the order to select and determine the array element E _IJK, and set each of the existing Latin body is the control unit for outputting a control signal according to a predetermined control program .

Reference numeral 2 denotes a control signal from the control unit 1,
A Latin cube storage array 12 in which the positions A _IJK are arranged corresponding to the Latin cube R to be created is formed, and the array element E _IJK at each position A _IJK of the Latin cube storage array 12 is formed. This is a Latin cube creation unit that selects and determines the symbol m by comparison.

The Latin cube creating section 2 determines the position A _IJK of the setting data, which is the signal m to be selected and determined, along the X axis I.
X-axis position designation section 3 for designating the Y-axis J of the setting data
A Y-axis position designating section 4 for designating a position A _IJK along
A Z-axis position specifying unit 5 that specifies a position _AIJK of the setting data along the Z-axis K, and a signal m that is compared with the setting data.
An X-axis position comparison unit 6 that specifies the position A _IJK along the X-axis I of the comparison data, and a Y-axis position comparison unit 7 that specifies the position A _IJK along the Y-axis J of the comparison data, A Z-axis position comparison unit 8 for designating a position A _IJK along the Z-axis K of the comparison data, a setting data storage unit, a setting data storage unit 9 for inputting / outputting, and a comparison data storage unit; An array element corresponding to a comparison data storage unit 10 for inputting / outputting, a data comparison unit 11 for performing a comparison operation of setting data and comparison data, and a Latin cube R of degree n of a required size. Position A for positioning E _IJK A _IJK is set and stored in a three-dimensionally arranged position setting Latin square storage array 1
2 and.

FIG. 17 shows an example of a flow chart of an embodiment of the invention described in claims 1 to 4, and in step S1, the control unit 1 is ordered with a degree n, a symbol m, and a symbol m. The order {0, 1, ... N-1} is specified, the X-axis position specifying unit 3 is at the beginning 1, the Y-axis position specifying unit 4 is at the beginning 1, and the Z-axis position specifying unit 5 is at the beginning 1. Set to.

In step S2, the initial value 0 of the symbol m of the Latin box R is set in the setting data storage unit 9 to set the array element E _IJK of each position A _IJK of the Latin box storage array 12. Set the value to the first value 0, step S3
If the value of the X-axis position designation section 3 is the first 1, there is no array element E _{IJK of} the same X-axis I to be compared, so the _{procedure proceeds} to step S5, where the array element E _IJK is , The Z-axis position comparison is performed by setting the value of the Y-axis position designation unit 4 in the Y-axis position comparison unit 7 so as to show the array element E _IJK of the previous position A _IJK arranged in the same X-axis I. The value of the Z-axis position designation section 5 is set in the section 8, and the X-axis position comparison section 6 is set.
Is sequentially changed from 1 to the previous value indicated by the position of the X-axis position specifying unit 3, and the comparison data storage unit 10 indicated by the value is changed.
Is compared with the value of the setting data storage unit 9 by the data comparison unit 11, and if there is a match, step S1
Go to 6.

In step S5, if the value of the Y-axis position designation section 4 is 1 at the beginning, there is no array element E _{IJK to} be compared along the same Y-axis J and before that.
Go to 7, step S6, the array element _{E IJK} is the sequence along the same Y axis J, it as shown an array element _{E IJK} previous position _{A IJK,} X-axis position in the X-axis position comparison section 6 The value of the designation unit 3 is set, the value of the Z-axis position designation unit 5 is set in the Z-axis position comparison unit 8, and the value of the Y-axis position comparison unit 7 is set from 1 to 1 indicating the position of the Y-axis position designation unit 4. The value in the comparison data storage unit 10 and the value in the setting data storage unit 9 are compared by the data comparison unit 11,
If there is a match, go to step S16.

In step S7, if the value of the Z-axis position designating section 5 is 1 at the beginning, there is no array element E _{IJK to} be compared along the same Z-axis K and before that, so step S9.
_Going to step S8, the array element E _IJK is arranged at the previous position A _IJK of the array element E _IJK along the same Z axis K.
_As indicated by _IJK , the value of the X-axis position specifying unit 3 is set in the X-axis position comparing unit 6 and the Y-axis position specifying unit 4 is set in the Y-axis position comparing unit 7.
Value is set, and the value of the Z-axis position comparison unit 8 is sequentially changed from 1 to the previous value indicated by the position of the Z-axis position designation unit 5,
The data comparison unit 11 compares the value of the comparison data storage unit 10 and the value of the setting data storage unit 9 that are shown, and if there is a match, the process proceeds to step S16.

A step S9 sets the setting value of the Z-axis position specifying unit 5 to the next value, and a step S10 determines whether the set value of the Z-axis position specifying unit 5 exceeds the final position A _IJn . If not, go to step S12.

A step S11 sets the setting value of the Y-axis position designating unit 4 to the next value and sets the setting value of the Z-axis position designating unit 5 to the value of the first 1, and a step S12 determines the Y-axis position. Whether or not the value of the designation section 4 exceeds the last position A _InK, and if not, go to step S14.

A step S13 sets the setting value of the X-axis position specifying unit 3 to the next value and sets the setting value of the Y-axis position specifying unit 4 to the value of the first 1, and a step S14 determines the X-axis position. Whether or not the value of the designated portion 3 has _exceeded the last position A _nJK, and if not, go to step S2, but if it does, the creation of the Latin _cube R is completed in step S15.

The step S16 sets the value of the array element E _{IJK at} the position A _IJK to the next value, and the step S17 determines that the value of the set array element E _IJK must exceed the last value (n-1). For example, go to step S3 and select the last value (n-1)
If it exceeds, there is nothing to put, so the operation proceeds to step S18.

In step S18, the setting data storage unit 9
By setting the first value 0 of the symbol m of the Latin cube R to, the value of the array element E _{IJK at} the position A _IJK is set to the first value 0.

A step S19 sets the set value of the Z-axis position specifying unit 5 to the previous value, and a step S20 determines that the set value of the Z-axis position specifying unit 5 is not before the first 1. Go to step S16.

A step S21 sets the value of the Y-axis position specifying unit 4 to the previous value and a value of the Z-axis position specifying unit 5 to the value n of the last position, and a step S22 returns Y. If the value of the axis position designation unit 4 is not before the first 1, go to step S16.

A step S23 sets the value of the X-axis position designating section 3 to the previous value, sets the value of the Y-axis position designating section 4 to the value n of the last position, and proceeds to step S16. , The selection and determination operation of the value of the array element E _IJK is repeated.

FIG. 18 shows an example of a flow chart of an embodiment of the invention described in claims 5 to 7, and step T1 is of the same order n as that for newly creating an array 12 for storing the Latin box. By storing the existing Latin cube of the same symbol m of
Symbol m, permutation of symbol m and selection order {0, 1, ... N-
1}, the X-axis position designation unit 3 is set to the last position value n, the Y-axis position designation unit 4 is set to the last position value n, and the Z-axis position designation unit 5 is set to the last position value n. Set to n.

Step T2 is an array 1 for storing a Latin box.
The value of the array element E _IJK of the position A _IJK of 2 is set to the next order of the symbol m of the Latin cube R, and the step T3 is the value of the array element E _IJK of the position A _IJK of the Latin cube storage array 12. Does not exceed the final value (n-1), the process proceeds to step T10. If the final value (n-1) is exceeded, there is nothing to put, so the process proceeds to step T4.

In step T4, the value 0 is set in the setting data storage unit 9 to set the value of the array element E _IJK of the position A _IJK of the Latin box storage array 12 to the initial value 0,
A step T5 sets the Z-axis position designating unit 5 to the previous position, and a step T6 goes to a step T2 when the Z-axis position designating unit 5 is not before the head 1.

In step T7, the Y-axis position designating section 4 is set to the previous position and the position of the Z-axis position designating section 5 is set to the last n. In step T8, the Y-axis position designating section 4 is set to the first position. If not earlier, go to step T2.

In step T9, the X-axis position designation section 3 is set to the previous position, and the Y-axis position designation section 4 is set to the last n.
Set to the position of and go to step T2.

In step T10, if the position of the X-axis position designation section 3 is the first position, there is no array element E _{IJK to} be compared in the same row on the X-axis I and before that, so step T12.
Go to step T11, compared value of the array element E _IJK, the same sequence of X-axis I, to indicate it array element E _IJK previous position A _IJK, Y-axis position in the Y-axis position comparator 7 The value of the designating section 4 is set, the value of the Z-axis position designating section 5 is designated to the Z-axis position comparing section 8, and the value of the X-axis position comparing section 6 is changed from 1 to X.
The value of the comparison data storage unit 10 and the value of the setting data storage unit 9 are sequentially changed by the data comparison unit 11 by changing the values up to the previous value indicated by the position of the axis position designation unit 3, and they match. If there is one, go to step T2.

In step T12, if the position of the Y-axis position designation section 4 is the head 1, there is no array element E _{IJK to} be compared in the same Y-axis J and before that, so step T14.
In step T13, the value of the array element E _IJK is set to the X-axis position comparison unit 6 so that the X-axis position comparison unit 6 indicates the array element E _IJK of the previous position A _{IJK in} the same array on the Y-axis J. The value of the designation unit 3 is set, the value of the Z-axis position designation unit 5 is set in the Z-axis position comparison unit 8, and the value of the Y-axis position comparison unit 7 is changed from 1 to Y.
The value of the comparison data storage unit 10 and the value of the setting data storage unit 9 that are shown are sequentially changed by the data comparison unit 11, and the values are matched. If there is one, go to step T2.

In step T14, if the position of the Z-axis position designation section 5 is the first position, there is no array element E _{IJK to} be compared with the same Z-axis K and the array elements E _{IJK to} be compared before that are set.
Go to step T15, compared value of the array element E _IJK, the same sequence of Z-axis K, which as shown the array element E _IJK previous position A _IJK, X-axis position in the X-axis position comparison section 6 The value of the designation unit 3 is set, the value of the Y-axis position designation unit 4 is set in the Y-axis position comparison unit 7, and the value of the Z-axis position comparison unit 8 is changed from 1 to Z.
The value of the comparison data storage unit 10 and the value of the setting data storage unit 9 are sequentially changed by the data comparison unit 11 by changing the values up to the previous value indicated by the position of the axis position designation unit 5 in sequence, and they match. If there is one, go to step T2.

In step T16, the position of the Z-axis position designating section 5 is set to the next position, and in step T17, the position of the Z-axis position designating section 5 exceeds or exceeds the final position A _IJK. If not, go to step T19.

In step T18, the Y-axis position designating section 4 is set to the next position, and the Z-axis position designating section 5 is set to the first position. In step T19, the Y-axis position designating section 4 is set. Whether or not the last position A _IJK has been exceeded, and if not, go to step T21.

In step T20, the X-axis position designating section 3 is set to the next position and the Y-axis position designating section 4 is set to the first position 1. In step T21, the X-axis position designating section 3 is set. Whether or not the last position A _IJK has been _exceeded , if not, the process proceeds to step T10, but if it is after the last position A _IJK , the process proceeds to step T22 to complete the creation.

[0054]

Since the present invention has the above-mentioned structure, it has the following effects. The invention according to claim 1 is
It is possible to regularly create a Latin cube of the desired degree and symbol, so that a Latin cube can be obtained reliably and easily.

The invention according to claim 2 can further enhance the certainty of regular production of the Latin cube.

The invention according to claim 3 greatly simplifies the digital processing in the invention according to claim 1 or 2,
The simplification of the arithmetic processing can be sufficiently achieved.

According to the fourth aspect of the invention, a standard Latin cube can be easily prepared.

According to the fifth aspect of the present invention, based on an existing Latin cube, all Latin cubes having the same degree and symbol can be regularly formed, whereby a large number of different degrees and symbols having the same degree can be obtained. It is possible to surely and easily obtain a Latin cube, expand the range of use of the Latin cube, and dramatically increase the utility value and utilization effect of the Latin cube.

According to the sixth aspect of the present invention, it is possible to reliably and easily obtain all the groups of Latin cubes having the same first row and first column and the same first depth. You can easily and surely create a large number of Latin cubes according to your purpose.

According to the invention described in claim 7, it is possible to obtain all the standard Latin cuboids of the orders and symbols to be set,
Therefore, it is possible to surely and easily obtain a large number of standard Latin cuboids that are most easily used.

[Brief description of drawings]

FIG. 1 is a diagram for explaining a primary Latin cube.

FIG. 2 is an explanatory diagram showing an example of a primary Latin cube.

FIG. 3 is a diagram for explaining a second-order Latin cube.

FIG. 4 is an explanatory diagram showing an example of a secondary Latin cube.

FIG. 5 is a diagram showing an example of a standard form used for the description of a cubic Latin cube.

FIG. 6 is a block diagram showing an electric circuit configuration of an apparatus configured to carry out the present invention.

7 is an explanatory diagram showing a configuration of a Latin rectangular storage array in the block diagram shown in FIG.

FIG. 8: Symbols as values of array elements of Latin cube are 0 to
Explanatory drawing which shows the example of arrangement set to 3.

FIG. 9: Symbols as values of array elements of Latin cube are 1 to
Explanatory drawing which shows the example of an arrangement set to 4.

FIG. 10 shows a symbol as a value of an array element of Latin cube
Explanatory drawing which shows the example of an array set as -d.

FIG. 11 is an explanatory diagram showing the order of positions for determining the values of array elements when creating a Latin cube.

FIG. 12 is another explanatory diagram showing the order of positions for determining the values of array elements when creating a Latin cube.

FIG. 13 is still another explanatory diagram showing the order of positions for determining the values of array elements when creating a Latin cube.

FIG. 14 is an explanatory diagram showing the order of positions for determining the values of array elements when creating a standard Latin box.

FIG. 15 is another explanatory diagram showing the order of positions for determining the values of array elements when creating a standard Latin box.

FIG. 16 is still another explanatory diagram showing the order of positions for determining the values of array elements when creating a standard Latin box.

FIG. 17 is a flowchart showing an operation procedure for creating a Latin box.

FIG. 18 is a flowchart showing an operation procedure for creating another Latin cube from an existing Latin cube.

[Explanation of symbols]

1; control unit 2; Latin cube creation unit 3; X-axis position designation unit 4; Y-axis position designation unit 5; Z-axis position designation unit 6; X-axis position comparison unit 7; Y-axis position comparison unit 8; Z-axis Position comparison unit 9; Setting data storage unit 10; Comparison data storage unit 11; Data comparison unit 12; Latin cube storage array R; Latin cube I; X axis J; Y axis K; Z axis A _IJK ; Position E _IJK ; Array element n; Order m; Symbol

─────────────────────────────────────────────────── ─── Continuation of the front page (56) References JP 10-105544 (JP, A) JP 10-10971 (JP, A) Koichi Yamamoto, “Various Phases of Latin Squares”, Mathematical Sciences, Japan, Stocks Company Science, June 1, 1979, Vo. 17, No. 6, p. 62-66 (58) Fields surveyed (Int.Cl. ⁷ , DB name) G09C 1/00 G06F 17/10

Claims (7)

(57) [Claims] 1. The order (n) of a Latin cube (R) to be created by arranging Latin squares in three dimensions (the vertical direction is the X axis, the horizontal direction is the Y axis, and the depth direction is the Z axis). A controller (1) for setting and setting a symbol (m) for the degree (n) in a permutation and a selection order according to the permutation, and the controller (1)
Corresponding to the order (n) set in
Latin _box creation unit (2) to set each position (A _IJK ) of 2)
And the Latin box producing unit (2),
According to a predetermined control program in (1), when selecting one of the symbols (m) as an array element (E _IJK ) at each position (A _IJK ) of the Latin rectangular storage array (12), The selection decision is made based on the X-axis (I) or Y-axis (J) or Z-axis (K).
Along the X-axis (I), Y-axis (J) and Z-axis (K) to the last position (A _IJK ) in order,
_The same X axis (I) and Y axis (J) and Z axis for each _IJK )
The previously determined array element at position (A _IJK ) before (K)
(E _IJK ) so that it is not the same symbol (m)
How to create a Latin cube that selects (m) in the order of selection. 2. For each position (A _IJK ), the already determined array element (E I) of the position (A _IJK ) before the same X-axis (I) and Y-axis (J) and Z-axis (K) is determined. _IJK ), when selecting the symbols (m) in order, so that they do not have the same symbol (m) as the desired position (A
When the symbol (m) is not capable of selecting and determining at _IJK) are already signs of array elements are determined (E _IJK) of the previous location of an arbitrary position (A _IJK) (A _IJK) The method for producing a Latin cube according to claim 1, wherein (m) is replaced with a selectable symbol (m) having a lower rank than the symbol (m) and the selection decision is continued. 3. The method for producing a Latin cube according to claim 1, wherein the selection order of the symbols (m) is set in the order of the permutations of the symbols (m). 4. A symbol of an array element (E _IJK ) at a position (A _IJK ) on a first X axis (I), a first Y axis (J) and a first Z axis (K).
(m) is set in advance to be the same as the standard Latin cube, and the remaining position
The selection decision of the symbol (m) of the array element (E _IJK ) of (A _IJK ),
The method for producing a Latin cube according to claim 1, 2 or 3, which is carried out in order from the position (A ₁₂₂ ) or the position (A ₂₁₂ ) or the position (A ₂₂₁ ). 5. The order (n) of a Latin cube (R) to be created by arranging the Latin squares in three dimensions (the vertical direction is the X axis, the horizontal direction is the Y axis, and the depth direction is the Z axis). A controller (1) for setting and setting a symbol (m) for the degree (n) in a permutation and a selection order according to the permutation, and the controller (1)
Corresponding to the order (n) set in
Latin _box creation unit (2) to set each position (A _IJK ) of 2)
And, setting the order (n) for the control unit (1), the permutation of the symbol (m) and the setting of the selection order according to the permutation, the Latin rectangular storage array (12) According to a control program that has been achieved by setting the existing Latin cube for the above, and is stored in advance in the control unit (1), the X-axis (I) and the Y-axis (J) of the Latin cube storage array (12) and Z axis (K)
From the last position (A _nnn ) of the X-axis (I) and Y-axis
Existing array elements (E _IJK ) along the (J) and Z-axis (K)
Returning to the order to the position where the selection order to select a symbol (m) is lower than the symbol (m) in (A _IJK), wherein from the position (A _IJK) X-axis (I) or a Y-axis (J) or Z Along the axis (K) up to the last position (A _nnn ), the same for each position (A _IJK ), the position before the X axis (I) and the Y axis (J) and the Z axis (K) (A
As already an array element being determined (E _IJK) does not equal symbol (m) of _IJK), symbol order array element (E _IJK)
How to create a Latin cube that selects and determines (m). 6. An X-axis (I), a Y-axis (J) and a Z-axis of a Latin cube storage array (12) in which an existing Latin cube is set.
From the last position (A _nnn ) of (K), the X-axis (I) and Y
Existing array elements along the axis (J) and Z axis (K)
A symbol (m) whose selection order is lower than the symbol (m) of (E _IJK ).
Return to the position (A _IJK ) where you can select, and the symbol of the array element (E _IJK ) from that position (A _IJK ) to the last position (A _nnn ).
(m) is selected and determined by determining the positions of the first X axis (I), the first Y axis (J) and the first Z axis (K) of the Latin rectangular storage array (12).
(A _IJK) other positions except for (A _IJK) how to create Latin of claim 5, wherein performing the subject. 7. The method for producing a Latin cube according to claim 6, wherein the existing Latin cube set in the Latin cube storage array (12) is a standard Latin cube.