Int. J. of Information and Coding Theory   »   2015 Vol.3, No.2

 

 

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

 

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

 

Submission date: 05 Jul 2015
Date of acceptance: 28 Jul 2015
Available online: 22 Oct 2015

 

 

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