On matrix-product structure of repeated-root constacyclic codes over finite fields

Authors: Yonglin Cao, Yuan Cao, Đinh Quang Hải, Fang-Wei Fu, Paravee Maneejuk,

https://doi.org/10.1016/j.disc.2019.111768

Publisher, magazine: ,

Publication year: 2020

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Abstract

For any prime number p, positive integers m,k,n, where n satisfies gcd(p,n)=1, and for any non-zero element λ0 of the finite field Fpm of cardinality pm, we prove that any λpk0-constacyclic code of length pkn over the finite field Fpm is monomially equivalent to a matrix-product code of a nested sequence of pkλ0-constacyclic codes with length n over Fpm. As an application, we completely determine the Hamming distances of all negacyclic codes of length 7⋅2l over F7 for any integer l≥3.

Tags: repeated-root constacyclic code; matrix-product code; monomially equivalent codes; finite chain ring