Optimal b-symbol constacyclic codes with respect to the Singleton bound
Optimal b-symbol constacyclic codes with respect to the Singleton bound
Source title:
Journal of Algebra and Its Applications, 2050151 (14 pages),
2020
(ISI)
Academic year of acceptance:
2019-2020
Abstract:
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 ηps, where b ≤ η and 0 ≤ i ≤ ps. As an application, all maximum distance separable (MDS) b-symbol constacyclic codes of length ηps 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.