An Algorithm to find the Generators of Multidimensional Cyclic Codes over a Finite Chain Ring

2023/03/14 by Disha Disha, Disha, Sucheta Dutt +1
Computer Science · #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Computer and information sciences #Information Theory (cs.IT)

paper · pdf · doi:10.48550/arxiv.2303.07881

openalex publication_date 2023/03/14 · openalex created_date 2023/03/17 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is to determine the algebraic structure of multidimensional cyclic codes over a finite chain ring \mathfrakR. An algorithm to find the generator polynomials of n dimensional (nD) cyclic codes of length m₁m₂… m_n over \mathfrakR has been developed using the generator polynomials of cyclic codes over \mathfrakR. Additionally, the generators of nD cyclic codes with length m₁m₂… m_n over \mathfrakR have been obtained as separable polynomials for the case q≡ 1(mod~ m_j), j≥ 2, where q=p^r is the cardinality of residue field of \mathfrakR.

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