Abstract

Let Fq 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 Fq such that γps=λ. In this paper, we determine the b-distance of λ-constacyclic codes with generator polynomials (xη−γ)i of length ηps, where b≤η and 0≤i≤ps. As an application, all maximum distance separable (MDS) b-symbol constacyclic codes of length ηps over Fq 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 ℓp, respectively, where ℓ is an odd prime.