New families of MDS symbol-pair codes from matrix-product codes

Abstract

In emerging storage technologies, the outputs of the channels consist of overlapping pairs of symbols. The errors are no longer individual symbols. Controlling them calls for a different approach. Symbol-pair codes have been proposed as a solution. The error-correcting capability of such a code depends on its minimum pair distance instead of the usual minimum Hamming distance. Longer codes can be conveniently constructed from known shorter ones by a matrix-product approach. The parameters of a matrix-product code can be determined from the parameters of the ingredient codes. We construct a new family of maximum distance separable (MDS) symbol-pair matrix-product codes. Codes which are permutation equivalent to matrix-product codes may have improved minimum pair distances. We present four new families of MDS symbol-pair codes and a new family of almost MDS symbol-pair codes. The codes in these five new families are permutation equivalent to matrix-product codes. Each of our five constructions identifies permutations that can increase the minimum pair distances. We situate the new families among previously known families of MDS symbol-pair codes to highlight the versatility of our matrix-product construction route.