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

Authors: 

Hai Q. Dinh, Xiaoqiang Wang, Jirakom Sirisrisakulchai

Source title: 
Journal of Algebra and Its Applications, 2050151 (14 pages), 2020 (ISI)
Academic year of acceptance: 
2019-2020
Abstract: 

Let a 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 a such that a. In this paper, we determine the b-distance of λ-constacyclic codes with generator polynomials a of length ηps, where bη and 0ips. As an application, all maximum distance separable (MDS) b-symbol constacyclic codes of length ηps over a 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.