LCP of group codes over finite Frobenius rings

被引：4
|
作者：
Liu, Xiusheng [1 ]
Liu, Hualu [2 ]
机构：
[1] Hubei Normal Univ, Coll Arts & Sci, Sch Sci & Technol, Huangshi 435109, Hubei, Peoples R China
[2] Hubei Univ Technol, Sch Sci, Wuhan 430068, Hubei, Peoples R China
来源：
DESIGNS CODES AND CRYPTOGRAPHY | 2023年 / 91卷 / 03期
关键词：
Finite Frobenius rings; LCP of group codes; Code equivalence; LINEAR COMPLEMENTARY PAIRS;
D O I：
10.1007/s10623-022-01120-5
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
A pair (C, D) of group codes in R[G] is called a linear complementary pair (abbreviated to LCP) if C circle plus D = R[G], where R is a finite Frobenius ring, and G is a finite group. We provide a necessary and sufficient condition for a pair (C, D) of group codes in R[G] to be LCP. Furthermore, we prove that if (C, D) is an LCP of group codes in R[G], then C and D-perpendicular to are permutation equivalent.
引用
收藏
页码：695 / 708
页数：14
相关论文
共 50 条
  • [31] CYCLIC CODES OVER LOCAL FROBENIUS RINGS OF ORDER 16
    Dougherty, Steven T.
    Kaya, Abidin
    Salturk, Esengul
    [J]. ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 2017, 11 (01) : 99 - 114
  • [32] Cyclic codes over finite rings
    Greferath, M
    [J]. DISCRETE MATHEMATICS, 1997, 177 (1-3) : 273 - 277
  • [33] Type Ⅱ codes over finite rings
    DOUGHERTY Steven T
    [J]. Science China Mathematics, 2010, (01) : 203 - 212
  • [34] Type Ⅱ codes over finite rings
    DOUGHERTY Steven T
    [J]. ScienceinChina(SeriesA:Mathematics)., 2010, 53 (01) - 212
  • [35] On the Equivalence of Codes over Finite Rings
    Hai Quang Dinh
    Sergio R. López-Permouth
    [J]. Applicable Algebra in Engineering, Communication and Computing, 2004, 15 : 37 - 50
  • [36] Cyclic Codes Over Finite Rings
    Qian, Jianfa
    [J]. 2011 7TH INTERNATIONAL CONFERENCE ON WIRELESS COMMUNICATIONS, NETWORKING AND MOBILE COMPUTING (WICOM), 2011,
  • [37] On the equivalence of codes over finite rings
    Dinh, HQ
    López-Permouth, SR
    [J]. APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 2004, 15 (01) : 37 - 50
  • [38] Constacyclic codes over finite local Frobenius non-chain rings with nilpotency index 3
    Castillo-Guillen, C. A.
    Renteria-Marquez, C.
    Tapia-Recillas, H.
    [J]. FINITE FIELDS AND THEIR APPLICATIONS, 2017, 43 : 1 - 21
  • [39] Duals of constacyclic codes over finite local Frobenius non-chain rings of length 4
    Castillo-Guillen, C. A.
    Renteria-Marquez, C.
    Tapia-Recillas, H.
    [J]. DISCRETE MATHEMATICS, 2018, 341 (04) : 919 - 933
  • [40] The linear programming bound for codes over finite Frobenius rings (vol 42, pg 289, 2007)
    Byrne, Eimear
    Greferath, Marcus
    O'Sullivan, Michael E.
    [J]. DESIGNS CODES AND CRYPTOGRAPHY, 2007, 45 (02) : 269 - +
12345