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Symbol-pair codes introduced by Cassuto and Blaum (2010) are designed to protect against pair errors in symbol-pair read channels. The higher the minimum pair distance, the more pair errors the code can correct. Maximum distance separable (MDS) symbol-pair codes are optimal in the sense that pair distance cannot be improved for given length and code size. The contribution of this paper is twofold. First, we present three lower bounds for the minimum pair distance of constacyclic codes, the first two of which generalize the previously known results due to Cassuto and Blaum (2011) and Kai et al. (2015). The third one exhibits a lower bound for the minimum pair distance of repeated-root cyclic codes. Second, we obtain new MDS symbol-pair codes with minimum pair distance seven and eight through repeated-root cyclic codes. [ABSTRACT FROM AUTHOR]

Let F q be the finite field with q elements and C n be the cyclic group of order n , where n is a positive integer relatively prime to q . Let H , K be subgroups of C n such that H is a proper subgroup of K . In this note, the weight distributions of the cyclic codes of length n over F q with generating idempotents K ˆ and e H , K = H ˆ − K ˆ are explicitly determined, where K ˆ = 1 / | K | ∑ g ∈ K g and H ˆ = 1 / | H | ∑ g ∈ H g . Our result naturally gives a new characterization of a theorem by Sharma and Bakshi [18] that determines the weight distribution of all irreducible cyclic codes of length p m over F q , where p is an odd prime and q is a primitive root modulo p m . Finally, two examples are presented to illustrate our results. [ABSTRACT FROM AUTHOR]