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

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 p^m, we prove that any -constacyclic code of length p^kn over the finite field  is monomially equivalent to a matrix-product code of a nested sequence of p^k λ₀-constacyclic codes with length n over . As an application, we completely determine the Hamming distances of all negacyclic codes of length 7⋅2^l over  for any integer l ≥ 3.