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

03/14/2023

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by   Disha, et al.

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The aim of this paper is to determine the algebraic structure of multidimensional cyclic codes over a finite chain ring ℜ. An algorithm to find the generator polynomials of n dimensional (nD) cyclic codes of length m_1m_2… m_n over ℜ has been developed using the generator polynomials of cyclic codes over ℜ. Additionally, the generators of nD cyclic codes with length m_1m_2… m_n over ℜ 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 ℜ.