New Families of MDS Symbol-Pair Codes From Matrix-Product Codes
Gaojun Luo, Martianus Frederic Ezerman, San Ling, Xu Pan
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.