Matrix-product structure of repeated-root constacyclic codes over finite fields

Abstract

For any prime number $p$, positive integers $m,k,n$ satisfying $\gcd (p,n)=1$ and ${\lambda }_0\in {\mathbb{F}}_{p^m}^{\times }$, we prove that any ${\lambda }_0^{p^k}$-constacyclic code of length $p^{k}n$ over the finite field ${\mathbb{F}}_{p^m}$ is monomially equivalent to a matrix-product code of a nested sequence of $p^k$ ${\lambda }_0$-constacyclic codes with length $n$ over ${\mathbb{F}}_{p^m}$.