Constructions of Maximum Distance Separable Symbol-Pair Codes Using Cyclic and Constacyclic Codes

TL;DR

This paper introduces new classes of maximum distance separable symbol-pair codes constructed from cyclic and constacyclic codes, enhancing error correction in symbol-pair read channels with specific minimum pair-distances.

Contribution

It presents novel constructions of MDS symbol-pair codes using cyclic and constacyclic codes, including a necessary and sufficient condition for cyclic codes to be MDS, and an algorithm for generating codes with higher pair-distance.

Findings

Constructed three new classes of MDS symbol-pair codes with pair-distance five or six.

Derived a necessary and sufficient condition for cyclic codes to be MDS symbol-pair codes.

Developed an algorithm to produce many MDS symbol-pair codes with pair-distance seven.

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.