Optimal b -symbol constacyclic codes with respect to the Singleton bound

Abstract

© 2020 World Scientific Publishing Company. Let q be the finite field of order q, where q is a power of odd prime p. Assume that γ, λ are nonzero elements of the finite field q such that γps = λ. In this paper, we determine the b-distance of λ-constacyclic codes with generator polynomials (xδ - γ)i of length δps, where b ≤ δ and 0 ≤ i ≤ ps. As an application, all maximum distance separable (MDS) b-symbol constacyclic codes of length δps over q are established. Among other results, we construct several classes of new MDS symbol-pair codes with minimum symbol-pair distance six or seven by using repeated-root cyclic codes of length 4p and p, respectively, where is an odd prime.