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

Authors: 

Yonglin Cao, Yuan Cao, Hai Q. Dinh, Fang-Wei Fu, Paravee Maneejuk

Source title: 
Discrete Mathematics, 343: 111768, 2020 (ISI)
Academic year of acceptance: 
2020-2021
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 1 of cardinality pm, we prove that any 1-constacyclic code of length pkn over the finite field 1 is monomially equivalent to a matrix-product code of a nested sequence of pk λ0-constacyclic codes with length n over a. As an application, we completely determine the Hamming distances of all negacyclic codes of length 7⋅2l over a for any integer l ≥ 3.