Two generalizations on the minimum Hamming distance of repeated-root constacyclic codes

Abstract

We study constacyclic codes, of length $n{p}^s$ and $2n{p}^s$, that are generated by the polynomials $(x^n+\gamma {)}^{\ell }$ and $(x^n-\xi {)}^i(x^n+\xi {)}^j$\ respectively, where $x^n+\gamma$, $x^n-\xi$ and $x^n+\xi$ are irreducible over the alphabet $\F_{p^a}$. We generalize the results of [5], [6] and [7] by computing the minimum Hamming distance of these codes. As a particular case, we determine the minimum Hamming distance of cyclic and negacyclic codes, of length $2p^s$, over a finite field of characteristic $p$.

We do not plan to publish the results of this paper on their own. We have put this paper for referring purposes