On the b-distance of repeated-root constacyclic codes of prime power lengths

Let p be a prime, s, m be positive integers, lambda be a nonzero element of the finite field F-pm. 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 lambda-constacyclic codes of length p(s) 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 lambda-constacyclic codes of length p(s), where 1 <= b <= left perpendicular p/2 right perpendicular. As an application, all MDS b-symbol constacyclic codes of length p(s) over F-pm are obtained. (C) 2019 Elsevier B.V. All rights reserved.