Abstract

Let be a prime, , be positive integers, be a nonzero element of the finite field . The -distance generalizes the Hamming distance , and the symbol-pair distance . While the Hamming and symbol-pair distances of all -constacyclic codes of length are completely determined, the general -distance of such codes was left opened. In this paper, we provide a new technique to establish the -distance of all -constacyclic codes of length , where . As an application, all MDS -symbol constacyclic codes of length over are obtained.