Linear codes over finite rings are trace codes

被引：1
|
作者：
Lu, Yaqi [1 ]
Shi, Minjia [1 ]
Greferath, Marcus [2 ]
Sole, Patrick [3 ]
机构：
[1] Anhui Univ, Sch Math Sci, Key Lab Intelligent Comp & Signal Proc, Minist Educ, Hefei 230601, Peoples R China
[2] Univ Coll Dublin, Sch Math & Stat, Dublin 4, Ireland
[3] Aix Marseille Univ, Cent Marseille, CNRS, I2M, F-13009 Marseilles, France
来源：
DISCRETE MATHEMATICS | 2020年 / 343卷 / 08期
基金：
中国国家自然科学基金;
关键词：
Finite ring; GF-trace; Basis; Linear codes; Cyclic codes; Trace representation; FEW-WEIGHT CODES; 2-WEIGHT;
D O I：
10.1016/j.disc.2020.111919
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Linear codes over finite rings are described here as trace codes for a suitable generalization of the trace called a GF-trace. Cyclic codes over Galois rings are given a trace description as well. The main tools are the notion of trace dual bases, in the case of linear codes, and of normal bases of an extension ring over a ring, in the case of cyclic codes. (C) 2020 Elsevier B.V. All rights reserved.
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页数：8
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