Z_4上长为2~s的负循环码的符号对距离
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摘要
符号对码是随着信息技术发展而产生的一种新型纠错码,它能对符号对读信道中符号对信息进行保护,符号对距离是衡量符号对码纠错能力的一个重要参数。文章利用Z_4上长为2~s的负循环码的结构和汉明距离,确立了Z_4上长为2~s的所有负循环码的符号对距离,给出了Z_4上长为2~s的负循环码的符号对距离分布。
Symbol-pair codes are a new kind of error-correcting codes with the development of information technology,which can protect symbol-pair information over symbol-pair read channels.For any symbol-pair code,the symbol-pair distance is an important parameter for measuring its pair-error-correcting capability.In this paper,the symbol-pair distance of negacyclic codes over Z_4 of length 2~s is studied.By using the structure and Hamming distance of such negacyclic codes,the symbol-pair distance of negacyclic codes over Z_4 of length 2~s is completely determined,and their symbol-pair distance distribution is given.
Symbol-pair codes are a new kind of error-correcting codes with the development of information technology,which can protect symbol-pair information over symbol-pair read channels.For any symbol-pair code,the symbol-pair distance is an important parameter for measuring its pair-error-correcting capability.In this paper,the symbol-pair distance of negacyclic codes over Z_4 of length 2~s is studied.By using the structure and Hamming distance of such negacyclic codes,the symbol-pair distance of negacyclic codes over Z_4 of length 2~s is completely determined,and their symbol-pair distance distribution is given.
引文
[1] CASSUTO Y,BLAUM M.Codes for symbol-pair read channels[J].IEEE Trans Inform Theory,2011,57(12):8011-8020.
[2] CASSUTO Y,LITSYN S.Symbol-pair codes:algebraic constructions and asymptotic bounds[C]//IEEE International Symposium on Information Theory Proceedings.[S.l.]:IEEE,2011:2348-2352.
[3] CHEE Y M,JI L J,KIAH H M,et al.Maximum distance separable codes for symbol-pair read channels[J].IEEE Trans Inform Theory,2013,59(11):7259-7267.
[4] KAI X S,ZHU S X,LI P.A construction of new MDS symbolpair codes[J].IEEE Trans Inform Theory,2015,61(11):5828-5834.
[5] LI S X,GE G N.Constructions of maximum distance separable symbol-pair codes using cyclic and constacyclic codes[J].Designs,Codes and Crypotographgy,2017,84(3):359-372.
[6] YAAKOBI E,BRUCK J,SIEGEL P H.Decoding of cyclic codes over symbol-pair read channels[C]//2012IEEE International Symposiumon on Information Theory Proceedings.[S.l.]:IEEE,2012:90-105.
[7] YAAKOBI E,BRUCK J,SIEGEL P H.Constructions and decoding of cyclic codes over b-symbol read channels[J].IEEE Trans Inform Theory,2016,62(4):1541-1551.
[8] DINH H Q.Complete distances of all negacyclic codes of length 2s over Z2a[J].IEEE Trans Inform Theory,2007,53(1):4252-4262.
[9] KAI X,ZHU S.On the distances of cyclic codes of length 2e over Z4[J].Discrete Mathematics,2010,310(1):12-20.
[10]施敏加,杨善林,朱士信.环F2+uF2+…+uk-1 F2上长为2s的(1+u)常循环码的距离分布[J].电子与信息学报,2010,32(1):112-116.
[11]朱士信,黄素娟.环Fpm+uFpm+…+uk-1 Fpm上(1+u)常循环码的齐次距离分布[J].电子与信息学报,2013,35(11):2579-2583.
[12]孙中华,朱士信,开晓山.环Z2m上一类常循环码的挠码及其应用[J].电子学报,2016,44(8):1826-1830.
[13]MCDONALD B R.Finite rings with identity[M].New York:Marcel Dekker,Inc,1974.
[2] CASSUTO Y,LITSYN S.Symbol-pair codes:algebraic constructions and asymptotic bounds[C]//IEEE International Symposium on Information Theory Proceedings.[S.l.]:IEEE,2011:2348-2352.
[3] CHEE Y M,JI L J,KIAH H M,et al.Maximum distance separable codes for symbol-pair read channels[J].IEEE Trans Inform Theory,2013,59(11):7259-7267.
[4] KAI X S,ZHU S X,LI P.A construction of new MDS symbolpair codes[J].IEEE Trans Inform Theory,2015,61(11):5828-5834.
[5] LI S X,GE G N.Constructions of maximum distance separable symbol-pair codes using cyclic and constacyclic codes[J].Designs,Codes and Crypotographgy,2017,84(3):359-372.
[6] YAAKOBI E,BRUCK J,SIEGEL P H.Decoding of cyclic codes over symbol-pair read channels[C]//2012IEEE International Symposiumon on Information Theory Proceedings.[S.l.]:IEEE,2012:90-105.
[7] YAAKOBI E,BRUCK J,SIEGEL P H.Constructions and decoding of cyclic codes over b-symbol read channels[J].IEEE Trans Inform Theory,2016,62(4):1541-1551.
[8] DINH H Q.Complete distances of all negacyclic codes of length 2s over Z2a[J].IEEE Trans Inform Theory,2007,53(1):4252-4262.
[9] KAI X,ZHU S.On the distances of cyclic codes of length 2e over Z4[J].Discrete Mathematics,2010,310(1):12-20.
[10]施敏加,杨善林,朱士信.环F2+uF2+…+uk-1 F2上长为2s的(1+u)常循环码的距离分布[J].电子与信息学报,2010,32(1):112-116.
[11]朱士信,黄素娟.环Fpm+uFpm+…+uk-1 Fpm上(1+u)常循环码的齐次距离分布[J].电子与信息学报,2013,35(11):2579-2583.
[12]孙中华,朱士信,开晓山.环Z2m上一类常循环码的挠码及其应用[J].电子学报,2016,44(8):1826-1830.
[13]MCDONALD B R.Finite rings with identity[M].New York:Marcel Dekker,Inc,1974.