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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 *ηp ^{s}*, where

*b*≤

*η*and

*0*≤

*i*≤

*p*. As an application, all maximum distance separable (MDS)

^{s}*b*-symbol constacyclic codes of length

*ηp*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 4

^{s}*p*and

*ℓp*, respectively, where

*ℓ i*s an odd prime.