CN110350924A

CN110350924A - A kind of construction of new (72,36,14) linear quasi-cyclic code

Info

Publication number: CN110350924A
Application number: CN201910721919.2A
Authority: CN
Inventors: 巫光福; 舒小俊; 江林伟; 乐植钢
Original assignee: Jiangxi University of Technology; China Railway Nanchang Group Co Ltd
Current assignee: Jiangxi University of Technology; China Railway Nanchang Group Co Ltd
Priority date: 2019-08-06
Filing date: 2019-08-06
Publication date: 2019-10-18
Anticipated expiration: 2039-08-06
Also published as: CN110350924B

Abstract

The invention discloses a kind of (72 newly, 36, 14) construction of linear quasi-cyclic code, it is related to the communications field, by using (72 to an input message sequence, 36) linear block codes battle array is encoded, export the coded sequence that length is 72, wherein, input information bit it is a length of 36 when, the minimum distance of the coded sequence of output is 14, the invention enables the minimum distances of quasi-cyclic code, and two are increased on the basis of original, system performance after improving linear block codes coding, network service quality and the speed of service for communication network field will be very helpful.

Description

A kind of construction of new (72,36,14) linear quasi-cyclic code

Technical field

The present invention relates to field of communication technology, the constructions of specially a kind of new (72,36,14) linear quasi-cyclic code.

Background technique

Stepped into information is social for current mankind, and communication is essential.It is required that a communications system transmission message is necessary Reliably and quickly, it is, however, required that quickly, then necessarily make that the time shared by each code element shortens, waveform narrows, energy is reduced, lead A possibility that cause generates mistake after being interfered increase, the reliability of message lower.Mostly using linear in Modern Communication System Block code encodes come the control information shorter to length.And for the linear block codes shorter for code length, minimum distance Size directly affect its error-correcting performance.The minimum range of code character is bigger, illustrates that the minimum differentiation between code word is bigger, anti-interference energy Power is stronger.Therefore people generally make its minimum distance reach theoretical maximum, at this time as far as possible when designing linear block codes The performance of linear block codes is optimal.But in equivalence class all structures of existing known 100 multiclass, 36 rank Hadamard matrix It produces self-dual [72,36,8], [72,36,12] error correcting code, therefore the performance of system is not optimal.

Summary of the invention

In view of the deficiencies of the prior art, the present invention provides the construction of a kind of new (72,36,14) linear quasi-cyclic code, Solve the problems, such as that above-mentioned background technique proposes.

The invention provides the following technical scheme: the construction of a kind of new (72,36,14) linear quasi-cyclic code, inputs to one Information sequence uses the linear block codes battle array of (72,36) to be encoded, the coded sequence that output length is 72, wherein defeated Enter information bit it is a length of 36 when so that output coded sequence minimum distance be 14；

Construct the matrix of G=(I | A), wherein the unit matrix that I is 36 × 36；

And the circular matrix that A is 36 × 36:

According to matrix G find out come minimum distance be 14；Circular matrix it is only necessary to know that matrix in the first row, Qi Tahang It can be obtained by the first row in cyclic shift, and the first row of matrix can regard one 36 binary numbers as, conversion An integer can be obtained at the decimal system, behind we with one big integer representation matrix A, A matrix as above can be write as integer 60327799。

Most preferably, the minimum range closer to theoretical code distance for having found (72,36) code is 14.

Most preferably, by G=(I | A), A matrix is that the code redistribution constructed according to integer 60327799 is

0:{1}

14:{9036}

16:{121716}

18:{1212396}

20:{9058338}

22:{52125372}

24:{231411882}

26:{803179548}

28:{2198817432}

30:{4781527704}

32:{8301694689}

34:{11541552984}

36:{12878054540}

38:{11541552984}

40:{8301694689}

42:{4781527704}

44:{2198817432}

46:{803179548}

48:{231411882}

50:{52125372}

52:{9058338}

54:{1212396}

56:{121716}

58:{9036}

72:{1}

Wherein preceding digital represents weight, and the number in { } represents the number of code word, such as 14:{ 9036 } weight is represented as 14 Code word number is 9036；

With the generator matrix G=of code redistribution having the same above (I | A), wherein A can also be following integer representation:

62620775,200163635,214443901,613261187,813591625,1320494245, 1385322169,1420920235,1760106775,1792067221,1951157131.

A matrix is that the code redistribution constructed according to integer 82472243 is

0:{1}

14:{9036}

16:{121959}

18:{1209468}

20:{9073620}

22:{52081740}

24:{231479265}

26:{803146716}

28:{2198758896}

30:{4781573208}

32:{8301956535}

34:{11540800440}

36:{12879054968}

38:{11540800440}

40:{8301956535}

42:{4781573208}

44:{2198758896}

46:{803146716}

48:{231479265}

50:{52081740}

52:{9073620}

54:{1209468}

56:{121959}

58:{9036}

72:{1}

107328185,608050009,649469705,1270107181,1483223735,1483225939, 1511593705,1521555139,1639204525,2323059865,2569596497.

A matrix is that the code redistribution constructed according to integer 83137423 is

0:{1}

14:{9036}

16:{122121}

18:{1207540}

20:{9083376}

22:{52056324}

24:{231504603}

26:{803198268}

28:{2198514240}

30:{4782049080}

32:{8301367323}

34:{11541348936}

36:{12878555040}

38:{11541348936}

40:{8301367323}

42:{4782049080}

44:{2198514240}

46:{803198268}

48:{231504603}

50:{52056324}

52:{9083376}

54:{1207540}

56:{122121}

58:{9036}

72:{1}

126765433,1120907413,1126976411,1152680863,1184547251,1263043559, 1418131873,1723968689,1827215969,2317628909,2437164523.

A matrix is that the code redistribution constructed according to integer 75310053 is

0:{1}

14:{9360}

16:{120114}

18:{1210564}

20:{9088542}

22:{52042212}

24:{231485136}

26:{803276640}

28:{2198499048}

30:{4781863536}

32:{8301570813}

34:{11541466872}

36:{12878211060}

38:{11541466872}

40:{8301570813}

42:{4781863536}

44:{2198499048}

46:{803276640}

48:{231485136}

50:{52042212}

52:{9088542}

54:{1210564}

56:{120114}

58:{9360}

72:{1}

87959025,104519835,113826531,296168775,351309525,359539173,475438257, 1457041677,1481018805,2611110789,2714125785.

A matrix is that the code redistribution constructed according to integer 77932509 is

0:{1}

14:{9360}

16:{119583}

18:{1216872}

20:{9056772}

22:{52123752}

24:{231411513}

26:{803072304}

28:{2199399984}

30:{4780089216}

32:{8303869863}

34:{11539163376}

36:{12880411544}

38:{11539163376}

40:{8303869863}

42:{4780089216}

44:{2199399984}

46:{803072304}

48:{231411513}

50:{52123752}

52:{9056772}

54:{1216872}

56:{119583}

58:{9360}

72:{1}

98510121,620662923,711182547,782287347,851767701,870367581,876765129, 1379436021,1473285669,4601829069,4671228489,4909788369,6020179089.

The present invention has following the utility model has the advantages that generator matrix has quasi- cyclic G=(I | A), and the transposition of A is equal to A；? 2 are increased on the basis of original (72,36) code minimum distance 12, the minimum distance of (72,36) code in this way is exactly 14.This says Its bright anti-interference ability enhances, and can correct the code with loop structure of 6 bit-errors.It is logical to thus reduce number The bit error rate in letter system and computer storage and arithmetic system, improves the reliability of digital communication, enhances systematicness Energy.The service quality and the speed of service of communication network in this way are significantly improved.

Detailed description of the invention

Fig. 1 is the present invention (72,36,14) Linear codes code submatrix A figure.

Specific embodiment

Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete Site preparation description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on Embodiment in the present invention, it is obtained by those of ordinary skill in the art without making creative efforts every other Embodiment shall fall within the protection scope of the present invention.

Referring to Fig. 1, (1) according to the A matrix in following Fig. 1 can obtain generator matrix G=(I | A) can construct (72, 36,14) linear block codes；

(2) since generator matrix wants system form, it is easy to obtain the check matrix H of code=(A | I)；

(3) the information m for being 36 according to the length to be transmitted, the code word c length after can must being encoded by generator matrix G are 72, c =m × G；

(4) code word c receives vector r by transmission, calculates syndrome s=r × HT according to check matrix

The transposition of HT expression check matrix H；

(5) the repairable error pattern table of code word is constructed according to check matrix, the t=6 in the error correcting capability of code includes altogether

A repairable error pattern；

(6) the error pattern e that syndrome s is found in table, is translated into c=r+e for r.

It should be noted that, in this document, relational terms such as first and second and the like are used merely to a reality Body or operation are distinguished with another entity or operation, are deposited without necessarily requiring or implying between these entities or operation In any actual relationship or order or sequence.Moreover, the terms "include", "comprise" or its any other variant are intended to Non-exclusive inclusion, so that the process, method, article or equipment including a series of elements is not only wanted including those Element, but also including other elements that are not explicitly listed, or further include for this process, method, article or equipment Intrinsic element.

It although an embodiment of the present invention has been shown and described, for the ordinary skill in the art, can be with A variety of variations, modification, replacement can be carried out to these embodiments without departing from the principles and spirit of the present invention by understanding And modification, the scope of the present invention is defined by the appended.

Claims

The construction of a kind of 1. new (72,36,14) linear quasi-cyclic code, which is characterized in that use an input message sequence The linear block codes battle array of (72,36) is encoded, the coded sequence that output length is 72, wherein a length of in input information bit When 36, so that the minimum distance of the coded sequence of output is 14；

Construct the matrix of G=(I | A), wherein the unit matrix that I is 36 × 36；

And the circular matrix that A is 36 × 36:

According to matrix G find out come minimum distance be 14；For circular matrix it is only necessary to know that matrix is in the first row, other rows can be with It is obtained by the first row in cyclic shift, and the first row of matrix can regard one 36 binary numbers as, be converted into ten System can obtain an integer, behind we with one big integer representation matrix A, A matrix as above can be write as integer 60327799。
The construction of a kind of new (72,36,14) 2. according to claim 1 linear quasi-cyclic code, which is characterized in that find The minimum range closer to theoretical code distance of (72,36) codes is 14.
The construction of a kind of new (72,36,14) 3. according to claim 1 linear quasi-cyclic code, which is characterized in that by G =(I | A), A matrix is that the code redistribution constructed according to integer 60327799 is

0:{1}

14:{9036}

16:{121716}

18:{1212396}

20:{9058338}

22:{52125372}

24:{231411882}

26:{803179548}

28:{2198817432}

30:{4781527704}

32:{8301694689}

34:{11541552984}

36:{12878054540}

38:{11541552984}

40:{8301694689}

42:{4781527704}

44:{2198817432}

46:{803179548}

48:{231411882}

50:{52125372}

52:{9058338}

54:{1212396}

56:{121716}

58:{9036}

72:{1}

Wherein preceding digital represents weight, and the number in { } represents the number of code word, such as 14:{ 9036 } weight is represented as 14 code word Number is 9036；

With the generator matrix G=of code redistribution having the same above (I | A), wherein A can also be following integer representation:

62620775,200163635,214443901,613261187,813591625,1320494245,1385322169, 1420920235,1760106775,1792067221,1951157131.

A matrix is that the code redistribution constructed according to integer 82472243 is

0:{1}

14:{9036}

16:{121959}

18:{1209468}

20:{9073620}

22:{52081740}

24:{231479265}

26:{803146716}

28:{2198758896}

30:{4781573208}

32:{8301956535}

34:{11540800440}

36:{12879054968}

38:{11540800440}

40:{8301956535}

42:{4781573208}

44:{2198758896}

46:{803146716}

48:{231479265}

50:{52081740}

52:{9073620}

54:{1209468}

56:{121959}

58:{9036}

72:{1}

With the generator matrix G=of code redistribution having the same above (I | A), wherein A can also be following integer representation:

107328185,608050009,649469705,1270107181,1483223735,1483225939, 1511593705,1521555139,1639204525,2323059865,2569596497.

A matrix is that the code redistribution constructed according to integer 83137423 is

0:{1}

14:{9036}

16:{122121}

18:{1207540}

20:{9083376}

22:{52056324}

24:{231504603}

26:{803198268}

28:{2198514240}

30:{4782049080}

32:{8301367323}

34:{11541348936}

36:{12878555040}

38:{11541348936}

40:{8301367323}

42:{4782049080}

44:{2198514240}

46:{803198268}

48:{231504603}

50:{52056324}

52:{9083376}

54:{1207540}

56:{122121}

58:{9036}

72:{1}

With the generator matrix G=of code redistribution having the same above (I | A), wherein A can also be following integer representation:

126765433,1120907413,1126976411,1152680863,1184547251,1263043559, 1418131873,1723968689,1827215969,2317628909,2437164523.

A matrix is that the code redistribution constructed according to integer 75310053 is

0:{1}

14:{9360}

16:{120114}

18:{1210564}

20:{9088542}

22:{52042212}

24:{231485136}

26:{803276640}

28:{2198499048}

30:{4781863536}

32:{8301570813}

34:{11541466872}

36:{12878211060}

38:{11541466872}

40:{8301570813}

42:{4781863536}

44:{2198499048}

46:{803276640}

48:{231485136}

50:{52042212}

52:{9088542}

54:{1210564}

56:{120114}

58:{9360}

72:{1}

With the generator matrix G=of code redistribution having the same above (I | A), wherein A can also be following integer representation:

87959025,104519835,113826531,296168775,351309525,359539173,475438257, 1457041677,1481018805,2611110789,2714125785.

A matrix is that the code redistribution constructed according to integer 77932509 is

0:{1}

14:{9360}

16:{119583}

18:{1216872}

20:{9056772}

22:{52123752}

24:{231411513}

26:{803072304}

28:{2199399984}

30:{4780089216}

32:{8303869863}

34:{11539163376}

36:{12880411544}

38:{11539163376}

40:{8303869863}

42:{4780089216}

44:{2199399984}

46:{803072304}

48:{231411513}

50:{52123752}

52:{9056772}

54:{1216872}

56:{119583}

58:{9360}

72:{1}

With the generator matrix G=of code redistribution having the same above (I | A), wherein A can also be following integer representation:

98510121,620662923,711182547,782287347,851767701,870367581,876765129, 1379436021,1473285669,4601829069,4671228489,4909788369,6020179089.