ON POLYCYCLIC CODES OVER A FINITE CHAIN RING

被引：18
|
作者：
Fotue-Tabue, Alexandre [1 ]
Martinez-Moro, Edgar [2 ]
Blackford, J. Thomas [3 ]
机构：
[1] Univ Yaounde I, Fac Sci, Yaounde, Cameroon
[2] Univ Valladolid, Inst Math, Edificio LUCIA,Campus Miguel Delibes, Valladolid 47011, Spain
[3] Western Illinois Univ, Dept Math, 1 Univ Circle, Macomb, IL 61455 USA
来源：
ADVANCES IN MATHEMATICS OF COMMUNICATIONS | 2020年 / 14卷 / 03期
关键词：
Galois extension of finite chain rings; polycyclic code; trace code; restriction code; CYCLIC CODES;
D O I：
10.3934/amc.2020028
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
Galois images of polycyclic codes over a finite chain ring S and their annihilator dual are investigated. The case when a polycyclic code is Galois-disjoint over the ring S, is characterized and, the trace codes and restrictions of free polycyclic codes over S are also determined giving an analogue of Delsarte's theorem relating the trace code and the annihilator dual code.
引用
收藏
页码：455 / 466
页数：12
相关论文
共 50 条
  • [1] On the Structure of Linear and Cyclic Codes over a Finite Chain Ring
    Graham H. Norton
    Ana Sălăgean
    Applicable Algebra in Engineering, Communication and Computing, 2000, 10 : 489 - 506
  • [2] On the Hamming distance of linear codes over a finite chain ring
    Norton, GH
    Salagean, A
    IEEE TRANSACTIONS ON INFORMATION THEORY, 2000, 46 (03) : 1060 - 1067
  • [3] Hulls of cyclic serial codes over a finite chain ring
    Talbi, Sarra
    Batoul, Aicha
    Tabue, Alexandre Fotue
    Martinez-Moro, Edgar
    FINITE FIELDS AND THEIR APPLICATIONS, 2022, 77
  • [4] On the structure of linear and cyclic codes over a finite chain ring
    Norton, GH
    Salagean, A
    APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 2000, 10 (06) : 489 - 506
  • [5] Cyclic codes over a non-commutative finite chain ring
    R. Sobhani
    Cryptography and Communications, 2018, 10 : 519 - 530
  • [6] On repeated-root multivariable codes over a finite chain ring
    Martinez-Moro, E.
    Rua, I. F.
    DESIGNS CODES AND CRYPTOGRAPHY, 2007, 45 (02) : 219 - 227
  • [7] Cyclic codes over a non-commutative finite chain ring
    Sobhani, R.
    CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES, 2018, 10 (03): : 519 - 530
  • [8] Two-dimensional cyclic codes over a finite chain ring
    Garg, Disha
    Dutt, Sucheta
    ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, 2024, 32 (03): : 75 - 88
  • [9] Cyclic self-orthogonal codes over finite chain ring
    Singh, Abhay Kumar
    Kumar, Narendra
    Shum, Kar Ping
    ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, 2018, 11 (06)
  • [10] Duadic negacyclic codes over a finite non-chain ring
    Goyal, Mokshi
    Raka, Madhu
    DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS, 2018, 10 (06)
12345