SKEW CONSTACYCLIC CODES OVER FINITE CHAIN RINGS

被引：76

作者：

Jitman, Somphong ^{[1
,2
]}

Ling, San ^{[2
]}

Udomkavanich, Patanee ^{[1
]}

机构：

[1] Chulalongkorn Univ, Dept Math & Comp Sci, Fac Sci, Bangkok 10330, Thailand

[2] Nanyang Technol Univ, Sch Phys & Math Sci, Div Math Sci, Singapore 637371, Singapore

来源：

ADVANCES IN MATHEMATICS OF COMMUNICATIONS | 2012年 / 6卷 / 01期

关键词：

Code over rings; skew constacyclic code; skew cyclic code; skew negacyclic code; finite chain ring; skew polynomial; CYCLIC CODES; NEGACYCLIC CODES; LENGTH 2(S); AUTOMORPHISMS;

D O I：

10.3934/amc.2012.6.39

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Skew polynomial rings over finite fields and over Galois rings have recently been used to study codes. In this paper, we extend this concept to finite chainrings. Properties of skew constacyclic codes generated by monic right divisors of x(n) - lambda, where lambda is a unit element, are exhibited. When lambda(2) = 1, the generators of Euclidean and Hermitian dual codes of such codes are determined together with necessary and sufficient conditions for them to be Euclidean and Hermitian self-dual. Specializing to codes over the ring F(p)m + uF(p)m, the structure of all skew constacyclic codes is completely determined. This allows us to express the generators of Euclidean and Hermitian dual codes of skew cyclic and skew negacyclic codes in terms of the generators of the original codes. An illustration of all skew cyclic codes of length 2 over F-3+uF(3) and their Euclidean and Hermitian dual codes is also provided.

引用

页码：39 / 63

页数：25

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