MDS Symbol-Pair Codes from Repeated-Root Cyclic Codes

TL;DR

This paper introduces two new classes of MDS symbol-pair codes derived from repeated-root cyclic codes, achieving higher minimum pair-distances than existing codes, thus enhancing error correction in pair-error channels.

Contribution

The paper presents novel MDS symbol-pair codes from repeated-root cyclic codes with larger minimum pair-distances than previously known codes.

Findings

Codes with minimum symbol-pair distance ten or twelve are constructed.

These codes outperform all known MDS symbol-pair codes from constacyclic codes.

The codes are based on repeated-root cyclic codes over finite fields with odd characteristic.

Abstract

Symbol-pair codes are proposed to combat pair-errors in symbol-pair read channels. The minimum symbol-pair distance is of significance in determining the error-correcting capability of a symbol-pair code. Maximum distance separable (MDS) symbol-pair codes are optimal in the sense that such codes can achieve the Singleton bound. In this paper, two new classes of MDS symbol-pair codes are proposed utilizing repeated-root cyclic codes over finite fields with odd characteristic. Precisely, these codes poss minimum symbol-pair distance ten or twelve, which is bigger than all the known MDS symbol-pair codes from constacyclic codes.