AMDS Symbol-Pair Codes from Repeated-Root Cyclic Codes

TL;DR

This paper constructs six new classes of AMDS symbol-pair codes using repeated-root cyclic codes, achieving optimal or near-optimal error correction capabilities with some codes having unbounded length and high minimum pair distance.

Contribution

It introduces six new classes of AMDS symbol-pair codes derived from repeated-root cyclic codes, expanding the known constructions and capabilities of such codes.

Findings

Six new classes of AMDS symbol-pair codes constructed

One class has unbounded length with minimum pair distance reaching 13

Codes improve error correction in symbol-pair read channels

Abstract

Symbol-pair codes are proposed to guard against 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. One of the central themes in symbol-pair coding theory is the constructions of symbol-pair codes with largest possible minimum pair distance. Maximum distance separable (MDS) and almost maximum distance separable (AMDS) symbol-pair codes are optimal and sub-optimal regarding to the Singleton bound, respectively. In this paper, six new classes of AMDS symbol-pair codes are explicitly constructed through repeated-root cyclic codes and one class of such codes has unbounded lengths and the minimum symbol-pair distance can reach $13$.