有限链环上一类常循环码的距离

袁健; 朱士信; 开晓山

doi:10.11999/JEIT160392

有限链环上一类常循环码的距离

doi: 10.11999/JEIT160392

基金项目:

国家自然科学基金(61370089, 60973125)，东南大学国家移动通信研究实验室开放研究基金(2014D04)，安徽省自然科学基金(1508085SQA198)

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- 被引次数: 0
出版历程
- 收稿日期: 2016-04-22
- 修回日期: 2016-09-23
- 刊出日期: 2017-03-19

On Distances of Family of Constacyclic Codes over Finite Chain Rings

Funds:

The National Natural Science Foundation of China (61370089, 60973125), The Open Research Fund of National Mobile Communications Research Laboratory, Southeast University (2014D04), The Natural Science Foundation of Anhui Province (1508085SQA198)

摘要

摘要: 在编码理论中，线性码的(最小)距离是一个极其重要的参数，它决定了码的纠错能力。设R为任一有限交换链环， a为其最大理想的一个生成元， R*为R的乘法单位群。对于任意wR*，该文利用R上任意长度的(1+aw)-常循环码的生成结构，通过计算这类码的高阶挠码，得到了R上任意长度的(1+aw)-常循环码的汉明距离，并研究了这类常循环码的齐次距离。这给编译有限链环上此类常循环码提供了重要的理论依据。
- 常循环码 /
- 有限链环 /
- 汉明距离 /
- 齐次距离
Abstract: In coding theory, the (minimum) distance of a code is a very important invariant, which always determines the error-correcting capability of the code. Let R be an arbitrary commutative finite chain ring, a is a generator of the unique maximal ideal andR* is the multiplicative group of units of R. In this paper, for any wR*, by using the generator polynomials of (1+aw)-constacyclic codes of any length over R, higher torsion codes of such codes are calculated. The Hamming distance of all(1+aw)-constacyclic codes of any length overR is determined and the exact homogeneous distance of some such codes is obtained. The result provides a theoretical basis for encoding and decoding for such constacyclic codes.
- Constacyclic codes /
- Finite chain rings /
- Hamming distance /
- Homogeneous distance

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参考文献(13)

HAMMONS A R Jr., KUMAR P V, CALDERBANK A R, et al. TheZ4-linearity of Kerdock, Preparata, Goethals and related codes[J]. IEEE Transactions on Information Theory, 1994, 40(2): 301-319. doi: 10.1109/18.312154.

施敏加, 杨善林, 朱士信. 环F2+uF2++uk-1F2上长度为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. doi: 10.3724/SP.J.1146.2008.01810.

SHI M J, YANG S L, and ZHU S X. The distributions of distances of (1+u)-constacyclic codes of length2s overF2+uF2++uk-1F2[J]. Journal of Electronics Information Technology, 2010, 32(1): 112-116. doi: 10.3724/ SP.J.1146.2008.01810.

KONG B, ZHENG X Y, and MA H J. The depth spectrums of constacyclic codes over finite chain rings[J]. Discrete Mathematics, 2015, 338(2): 256-261. doi: 10.1016/j.disc.2014. 09.013.

QIAN K Y, ZHU S X, and KAI X S. On cyclic self-orthogonal codes over Z2m[J]. Finite Fields and Their Applications, 2015, 33: 53-65. doi: 10.1016/j.ffa.2014.11.005.

DINH H Q, DHOMPONGSA S, and SRIBOONCHITTA S. Repeated-root constacyclic codes of prime power length overFpm[u]/ua and their duals[J]. Discrete Mathematics, 2016, 339(6): 1706-1715. doi: 10.1016/j.disc.2016.01.020.

WOLFMANN J. Negacyclic and cyclic codes over Z4[J]. IEEE Transactions on Information Theory, 1999, 45(7): 2527-2532. doi: 10.1109/18.796397.

NORTON G H andSǎLǎGAN A. On the structure of linear and cyclic codes over a finite chain ring[J]. Applicable Algebra in Engineering, Communication and Computing, 2000, 10(6): 489-506. doi: 10.1007/PL00012382.

NORTON G H and SǎLǎGAN A. On the Hamming distance of linear codes over a finite chain ring[J]. IEEE Transactions on Information Theory, 2000, 46(3): 1060-1067. doi: 10.1109/18.841186.

GREFERATH M and SCHMIDT S E. Gray isometries for finite chain rings and a nonlinear ternary (36,312,15)code[J]. IEEE Transactions on Information Theory, 1999, 45(7): 2522-2524. doi: 10.1109/18.796395.

CAO Y L. On constacyclic codes over finite chain rings[J]. Finite Fields and Their Applications, 2013, 24: 124-135. doi: 10.1016/j.ffa.2013.07.001.

MCDONALD B R. Finite Rings with Identity[M]. New York, Marcel Dekker Press, 1974: 56-97.

DINH H Q. Constacyclic codes of lengthps over Fpm+uFpm[J]. Journal of Algebra, 2010, 324(5): 940-950. doi: 10.1016/j.jalgebra.2010.05.027.

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