Hamming Distance of Constacyclic Codes of Length <italic>p^s</italic> Over F_{<italic>p^m</italic>}&#x002B;<italic>u</italic>F_{<italic>p^m</italic>}&#x002B;<italic>u</italic>&#x00B2;F_{<italic>p^m</italic>}

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 $p^s$ over the finite commutative chain ring $\mathbb {F}_{p^m}+ u\mathbb {F}_{p^m} + u^{2}\mathbb {F}_{p^m}\,\,\, (u^3=0)$ . As applications, we identify all maximum distance saparable codes (i.e., optimal codes with respect to the Singleton bound) among them.

Keywords

• Hamming distance
• constacyclic codes
• optimal codes
• MDS codes