On codes over product of finite chain rings

被引：2
作者：
Bajalan, Maryam [1 ]
Rezaei, Rashid [1 ]
Samei, Karim [2 ]
机构：
[1] Malayer Univ, Dept Math, Malayer 65719, Iran
[2] Bu Ali Sina Univ, Dept Math, Hamadan 65175, Iran
来源：
SIGMA JOURNAL OF ENGINEERING AND NATURAL SCIENCES-SIGMA MUHENDISLIK VE FEN BILIMLERI DERGISI | 2023年 / 41卷 / 01期
关键词：
MDS Codes; Self-Dual Codes; Chain Rings; CYCLIC CODES;
D O I：
10.14744/sigma.2023.00014
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
In this paper, codes over the direct product of two finite commutative chain rings are studied. The standard form of the parity-check matrix is determined. The structure of self-dual codes is described. A distance preserving Gray map from the direct product of chain rings to a finite field is defined. Two upper bounds on minimum distance are obtained.
引用
收藏
页码：143 / 153
页数：11
相关论文
共 30 条
  • [1] Aydogdu I., 2019, J. Algebra Comb. Discrete Appl., V6, P39, DOI [10.13069/jacodesmath.514339, DOI 10.13069/JACODESMATH.514339]
  • [2] On the structure of Z2Z2[u3]-linear and cyclic codes
    Aydogdu, Ismail
    Siap, Irfan
    Ten-Valls, Roger
    [J]. FINITE FIELDS AND THEIR APPLICATIONS, 2017, 48 : 241 - 260
  • [3] On Zpr Zps-additive codes
    Aydogdu, Ismail
    Siap, Irfan
    [J]. LINEAR & MULTILINEAR ALGEBRA, 2015, 63 (10) : 2089 - 2102
  • [4] Aydogdu I, 2015, INT J COMPUT MATH, V92, P1806, DOI 10.1080/00207160.2013.859854
  • [5] Bilal M, 2011, DESIGN CODE CRYPTOGR, V61, P31, DOI 10.1007/s10623-010-9437-1
  • [6] Linear and cyclic codes over direct product of finite chain rings
    Borges, J.
    Fernandez-Cordoba, C.
    Ten-Valls, R.
    [J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2018, 41 (16) : 6519 - 6529
  • [7] Borges J, 2018, DESIGN CODE CRYPTOGR, V86, P1377, DOI 10.1007/s10623-017-0401-1
  • [8] Z2Z4-Additive Cyclic Codes, Generator Polynomials, and Dual Codes
    Borges, Joaquim
    Fernandez-Cordoba, Cristina
    Ten-Valls, Roger
    [J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2016, 62 (11) : 6348 - 6354
  • [9] Constantinescu I., 1997, Problems of Information Transmission, V33, P208
  • [10] SOME RESULTS ON ZpZp[v]-ADDITIVE CYCLIC CODES
    Diao, Lingyu
    Gao, Jian
    Lu, Jiyong
    [J]. ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 2020, 14 (04) : 555 - 572
123