Additive cyclic codes over finite commutative chain rings

被引：5
|
作者：
Martinez-Moro, Edgar [1 ]
Otal, Kamil [2 ,3 ]
Ozbudak, Ferruh [2 ,3 ]
机构：
[1] Univ Valladolid, Math Res Inst, Castilla, Spain
[2] Middle East Tech Univ, Dept Math, Dumlupmar Bulvari 1, TR-06800 Ankara, Turkey
[3] Middle East Tech Univ, Inst Appl Math, Dumlupmar Bulvari 1, TR-06800 Ankara, Turkey
来源：
DISCRETE MATHEMATICS | 2018年 / 341卷 / 07期
关键词：
Cyclic codes; Additive codes; Codes over rings; Finite commutative chain rings; Galois rings; MULTIVARIABLE CODES; GALOIS RINGS; CONSTRUCTION; PREPARATA; KERDOCK;
D O I：
10.1016/j.disc.2018.03.016
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Additive cyclic codes over Galois rings were investigated in Cao et al. (2015). In this paper, we investigate the same problem but over a more general ring family, finite commutative chain rings. When we focus on non-Galois finite commutative chain rings, we observe two different kinds of additivity. One of them is a natural generalization of the study in Cao et al. (2015), whereas the other one has some unusual properties especially while constructing dual codes. We interpret the reasons of such properties and illustrate our results giving concrete examples. (C) 2018 Elsevier B.V. All rights reserved.
引用
收藏
页码：1873 / 1884
页数：12
相关论文
共 50 条
  • [1] Notes on Linear Codes over Finite Commutative Chain Rings
    Zi-hui Liu Department of Mathematics
    [J]. Acta Mathematicae Applicatae Sinica, 2011, 27 (01) : 141 - 148
  • [2] Notes on linear codes over finite commutative chain rings
    Zi-hui Liu
    [J]. Acta Mathematicae Applicatae Sinica, English Series, 2011, 27 : 141 - 148
  • [3] Notes on linear codes over finite commutative chain rings
    Liu, Zi-hui
    [J]. ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES, 2011, 27 (01): : 141 - 148
  • [4] Cyclic and negacyclic codes over finite chain rings
    Dinh, HQ
    López-Permouth, SR
    [J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2004, 50 (08) : 1728 - 1744
  • [5] On the lattice of cyclic codes over finite chain rings
    Fotue-Tabue, Alexandre
    Mouaha, Christophe
    [J]. ALGEBRA AND DISCRETE MATHEMATICS, 2019, 27 (02): : 252 - 268
  • [6] Constacyclic and cyclic codes over finite chain rings
    QIAN Jian-fa
    [J]. The Journal of China Universities of Posts and Telecommunications, 2009, 16 (03) : 122 - 125
  • [7] Contraction of cyclic codes over finite chain rings
    Tabue, Alexandre Fotue
    Mouaha, Christophe
    [J]. DISCRETE MATHEMATICS, 2018, 341 (06) : 1722 - 1731
  • [8] On Isodual Cyclic Codes over Finite Chain Rings
    Batoul, Aicha
    Guenda, Kenza
    Gulliver, T. Aaron
    Aydin, Nuh
    [J]. CODES, CRYPTOLOGY AND INFORMATION SECURITY, C2SI 2017, 2017, 10194 : 176 - 194
  • [9] On the Construction of Quantum and LCD Codes from Cyclic Codes over the Finite Commutative Rings
    Ali, Shakir
    Alali, Amal S.
    Jeelani, Mohammad
    Kurulay, Muhammet
    oeztas, Elif Segah
    Sharma, Pushpendra
    [J]. AXIOMS, 2023, 12 (04)
  • [10] On the enumeration and classification of σ-LCD codes over finite commutative chain rings
    Yadav, Monika
    Sharma, Anuradha
    [J]. DISCRETE MATHEMATICS, 2022, 345 (08)
12345