Constacyclic symbol-pair codes: lower bounds and optimal constructions

TL;DR

This paper establishes new lower bounds for the minimum pair distance of constacyclic codes and constructs new MDS symbol-pair codes with higher pair distances, advancing error correction capabilities in symbol-pair read channels.

Contribution

It introduces three generalized lower bounds for the minimum pair distance of constacyclic codes and constructs new MDS symbol-pair codes with pair distances seven and eight.

Findings

Three new lower bounds for pair distance of constacyclic codes

New MDS symbol-pair codes with pair distances 7 and 8

Generalization of previous bounds for repeated-root cyclic codes

Abstract

Symbol-pair codes introduced by Cassuto and Blaum (2010) are designed to protect against pair errors in symbol-pair read channels. The higher the minimum pair distance, the more pair errors the code can correct. MDS symbol-pair codes are optimal in the sense that pair distance cannot be improved for given length and code size. The contribution of this paper is twofold. First we present three lower bounds for the minimum pair distance of constacyclic codes, the first two of which generalize the previously known results due to Cassuto and Blaum (2011) and Kai {\it et al.} (2015). The third one exhibits a lower bound for the minimum pair distance of repeated-root cyclic codes. Second we obtain new MDS symbol-pair codes with minimum pair distance seven and eight through repeated-root cyclic codes.