Title: Double cyclic codes over 𝔽q + u𝔽q + u2𝔽q

Authors: Ting Yao; Minjia Shi; Patrick Solé

Addresses: Key Laboratory of Intelligent Computing Signal Processing Ministry of Education, Anhui University, No. 3, Feixi Road, Hefei, Anhui Province 230039, P.R. China; School of Mathematical Sciences, Anhui University, Anhui 230601, P.R. China ' Key Laboratory of Intelligent Computing Signal Processing Ministry of Education, Anhui University, No. 3, Feixi Road, Hefei, Anhui Province 230039, P.R. China; School of Mathematical Sciences, Anhui University, Anhui 230601, P.R. China ' Telecom Paris Tech, Paris, France

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 Rr × Rs. In this paper, the generator polynomials of this family of codes as R[x]-submodules of Rr × Rs are determined. Further, the minimal generating sets of this family of codes as R-submodules of Rr × Rs are obtained. Finally, we show the relationship of generators between the double cyclic code and its dual.

Keywords: double cyclic codes; generator polynomials; minimal generating sets; dual codes; chain rings.

DOI: 10.1504/IJICOT.2015.072637

International Journal of Information and Coding Theory, 2015 Vol.3 No.2, pp.145 - 157

Available online: 22 Oct 2015

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