On the [formula omitted]-distance of repeated-root constacyclic codes of prime power lengths

Abstract

Let p be a prime, s, m be positive integers, λ be a nonzero element of the finite field Fpm. The b-distance generalizes the Hamming distance (b=1), and the symbol-pair distance (b=2). While the Hamming and symbol-pair distances of all λ-constacyclic codes of length ps are completely determined, the general b-distance of such codes was left opened. In this paper, we provide a new technique to establish the b-distance of all λ-constacyclic codes of length ps, where 1≤b≤⌊p2⌋. As an application, all MDS b-symbol constacyclic codes of length ps over Fpm are obtained.