Constructions of Maximum Distance Separable Symbol-Pair Codes Using Cyclic and Constacyclic Codes
Abstract
Symbol-pair code is a new coding framework which is proposed to correct errors in the symbol-pair read channel. In particular, maximum distance separable (MDS) symbol-pair codes are a kind of symbol-pair codes with the best possible error-correction capability. Employing cyclic and constacyclic codes, we construct three new classes of MDS symbol-pair codes with minimum pair-distance five or six. Moreover, we find a necessary and sufficient condition which ensures a class of cyclic codes to be MDS symbol-pair codes. This condition is related to certain property of a special kind of linear fractional transformations. A detailed analysis on these linear fractional transformations leads to an algorithm, which produces many MDS symbol-pair codes with minimum pair-distance seven.
Cite
@article{arxiv.1608.02687,
title = {Constructions of Maximum Distance Separable Symbol-Pair Codes Using Cyclic and Constacyclic Codes},
author = {Shuxing Li and Gennian Ge},
journal= {arXiv preprint arXiv:1608.02687},
year = {2016}
}
Comments
16 pages, Designs, Codes, and Cryptography, Accepted