Double cyclic codes over 𝔽q + u𝔽q + u2𝔽q. (2015)

• Record Type: Journal Article
• Authors: Yao, Ting; Shi, Minjia; Solé, Patrick
• Is Part Of: International journal of information and coding theory. Volume 3:Number 2(2015)
• Page Start: 145
• Page End: 157
• Publication Date: 2015
• Subjects: double cyclic codes -- generator polynomials -- minimal generating sets -- dual codes -- chain rings; Coding theory -- Periodicals; Information theory -- Periodicals; 003.54
• Languages: English
• ISSNs: 1753-7703

Abstract

A double cyclic code of length (r, s) over a chain ring R is a set that can be partitioned into two parts that any cyclic shift of the coordinates of both parts leaves invariant the code. These codes can be viewed as R[x]-submodules of R r × R s . In this paper, the generator polynomials of this family of codes as R[x]-submodules of R r × R s are determined. Further, the minimal generating sets of this family of codes as R-submodules of R r × R s are obtained. Finally, we show the relationship of generators between the double cyclic code and its dual.