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

Let  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  such that . In this paper, we determine the b-distance of λ-constacyclic codes with generator polynomials  of length ηp^s, where b ≤ η and 0 ≤ i ≤ p^s. As an application, all maximum distance separable (MDS) b-symbol constacyclic codes of length ηp^s over  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.