Cyclic codes over M2(F2 + uF2)

被引：0

作者：

Luo, Rong ^{[1
]}

Parampalli, Udaya ^{[2
]}

机构：

[1] Southwest Jiaotong Univ, Sch Math, Chengdu 610031, Sichuan, Peoples R China

[2] Univ Melbourne, Dept Comp & Informat Syst, Melbourne, Vic 3010, Australia

来源：

CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES | 2018年 / 10卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Cyclic codes; Lee weight; Bachoc weight; Gray map; RINGS;

D O I：

10.1007/s12095-017-0266-1

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Let A = M-2(F-2 + uF(2)), where u(2) = 0, the ring of 2 x 2 matrices over the finite ring F-2 + uF(2). The ring A is a non-commutative Frobenius ring but not a chain ring. In this paper, we derive the structure theorem of cyclic codes of odd length over the ring A and use them to construct some optimal cyclic codes over F-4. Let v(2) = 0 and uv = vu. We also give an isometric map from A to F-4 + vF(4) + uF(4) + uvF(4) using their respective Bachoc weight and Lee weight.

引用

页码：1109 / 1117

页数：9

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