Linear complementary pairs of codes over rings

被引：13
作者：
Hu, Peng [1 ]
Liu, Xiusheng [1 ,2 ]
机构：
[1] Hubei Polytech Univ, Sch Math & Phys, Huangshi 435003, Hubei, Peoples R China
[2] Hubei Normal Univ, Sch Sci & Technol, Coll Arts & Sci, Huangshi 435109, Hubei, Peoples R China
来源：
DESIGNS CODES AND CRYPTOGRAPHY | 2021年 / 89卷 / 11期
关键词：
Chain rings; LCP of codes; Constacylic codes; Generating polynomials; CYCLIC CODES; LCD CODES; DUAL CODES; FINITE;
D O I：
10.1007/s10623-021-00933-0
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
In this work, we first prove a necessary and sufficient condition for a pairs of linear codes over finite rings to be linear complementary pairs (abbreviated to LCPs). In particular, a judging criterion of free LCP of codes over finite commutative rings is obtained. Using the criterion of free LCP of codes, we construct a maximum-distance-separable (MDS) LCP of codes over ring Z(4). Then, all the possible LCP of codes over chain rings are determined. We also generalize the criterions for constacyclic and quasi-cyclic LCP of codes over finite fields to constacyclic and quasi-cyclic LCP of codes over chain rings. Finally, we give a characterization of LCP of codes over principal ideal rings. Under suitable conditions, we also obtain the judging criterion for a pairs of cyclic codes over principal ideal rings Z(k) to be LCP, and illustrate a MDS LCP of cyclic codes over the principal ideal ring Z(15).
引用
收藏
页码：2495 / 2509
页数：15
相关论文
共 31 条
[1]   Do non-free LCD codes over finite commutative Frobenius rings exist? [J].
Bhowmick, Sanjit ;
Fotue-Tabue, Alexandre ;
Martinez-Moro, Edgar ;
Bandi, Ramakrishna ;
Bagchi, Satya .
DESIGNS CODES AND CRYPTOGRAPHY, 2020, 88 (05) :825-840
[2]   A note on linear complementary pairs of group codes [J].
Borello, Martino ;
de la Cruz, Javier ;
Willems, Wolfgang .
DISCRETE MATHEMATICS, 2020, 343 (08)
[3]   On Linear Complementary Pairs of Codes [J].
Carlet, Claude ;
Guneri, Cem ;
Ozbudak, Ferruh ;
Ozkaya, Buket ;
Sole, Patrick .
IEEE TRANSACTIONS ON INFORMATION THEORY, 2018, 64 (10) :6583-6589
[4]   Complementary Dual Codes for Counter-Measures to Side-Channel Attacks [J].
Carlet, Claude ;
Guilley, Sylvain .
CODING THEORY AND APPLICATIONS, 4TH INTERNATIONAL CASTLE MEETING, 2015, 3 :97-105
[5]   COMPLEMENTARY DUAL CODES FOR COUNTER-MEASURES TO SIDE-CHANNEL ATTACKS [J].
Carlet, Claude ;
Guilley, Sylvain .
ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 2016, 10 (01) :131-150
[6]   On group codes with complementary duals [J].
de la Cruz, Javier ;
Willems, Wolfgang .
DESIGNS CODES AND CRYPTOGRAPHY, 2018, 86 (09) :2065-2073
[7]  
Dougherty S.T., 2011, MATH J OKAYAMA U, V53, P39
[8]   Independence of vectors in codes over rings [J].
Dougherty, Steven T. ;
Liu, Hongwei .
DESIGNS CODES AND CRYPTOGRAPHY, 2009, 51 (01) :55-68
[9]   MDS codes over finite principal ideal rings [J].
Dougherty, Steven T. ;
Kim, Jon-Lark ;
Kulosman, Hamid .
DESIGNS CODES AND CRYPTOGRAPHY, 2009, 50 (01) :77-92
[10]   Matrix product codes over finite commutative Frobenius rings [J].
Fan, Yun ;
Ling, San ;
Liu, Hongwei .
DESIGNS CODES AND CRYPTOGRAPHY, 2014, 71 (02) :201-227
1234