Hamming distance of constacyclic codes of length p^sover F<inf>p</inf>^mCuF<inf>p</inf>^mCu²Fp^m

Abstract

Let $p$ be any prime, $s$ and $m$ be positive integers. In this paper, we completely determine the Hamming distance of all constacyclic codes of length ps$ over the finite commutative chain ring $\mathbb {F}{pm}+ u\mathbb {F}{pm} + u{2}\mathbb {F}{pm}\,\,\, (u3=0)$. As applications, we identify all maximum distance saparable codes (i.e., optimal codes with respect to the Singleton bound) among them.