On matrix-product structure of repeated-root constacyclic codes over finite fields
On matrix-product structure of repeated-root constacyclic codes over finite fields
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 of cardinality pm, we prove that any
-constacyclic code of length pkn over the finite field
is monomially equivalent to a matrix-product code of a nested sequence of pk λ0-constacyclic codes with length n over
. As an application, we completely determine the Hamming distances of all negacyclic codes of length 7⋅2l over
for any integer l ≥ 3.