Abstract
Let [Formula: see text] be the finite field of order [Formula: see text], where [Formula: see text] is a power of odd prime [Formula: see text]. Assume that [Formula: see text], [Formula: see text] are nonzero elements of the finite field [Formula: see text] such that [Formula: see text]. In this paper, we determine the [Formula: see text]-distance of [Formula: see text]-constacyclic codes with generator polynomials [Formula: see text] of length [Formula: see text], where [Formula: see text] and [Formula: see text]. As an application, all maximum distance separable (MDS) [Formula: see text]-symbol constacyclic codes of length [Formula: see text] over [Formula: see text] 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 [Formula: see text] and [Formula: see text], respectively, where [Formula: see text] is an odd prime.
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