On Repeated-Single-Root Constacyclic Codes

Abstract

A new derivation is presented for the minimum Hamming distance of a class of p^r-ary maximum distance separable constacyclic codes (n = p, k, d = p - k + 1), where p is a prime and r is a positive integer, introduced by Massey, Costello, and Justesen in 1973. These are repeated-single-root constacyclic codes generated by the polynomial g(x) = (x - a) ^p-k, 1 ≤ k < p, a ≠ 0, a ∈ GF(p^r). As a by-product of the derivation for the minimum Hamming distance these codes are shown to be equivalent to shortened generalized Reed-Solomon codes. An application of these codes is suggested for secret-key cryptosystems.