A new class of MDS symbol-pair codes

TL;DR

This paper introduces a new class of MDS symbol-pair codes inspired by Reed-Solomon codes, achieving optimal parameters and analyzing their weight distributions for certain cases, advancing coding theory for pair-error channels.

Contribution

The paper constructs a novel class of q-ary MDS symbol-pair codes with specific parameters, extending classical Reed-Solomon code constructions to symbol-pair coding.

Findings

Constructed q-ary MDS symbol-pair codes with explicit parameters

Determined symbol-pair weight distributions for codes with k=3,4

Extended classical Reed-Solomon code ideas to symbol-pair coding

Abstract

The symbol-pair code is a new coding framework proposed to guard against pair-errors in symbol-pair read channels. Especially, a symbol-pair code with the parameters achieving the Singleton-type bound is called an MDS symbol-pair code. In this paper, inspiring by the classical construction for Reed-Solomon codes, for any $3\le k<m\le q-2$ and $m_1=\Big\lfloor{\tiny\frac{m}{\lfloor\frac{k-1}{2}\rfloor}}\Big\rfloor$, we construct a class of $q$-ary MDS symbol-pair codes with dimension $k$ and length $n$ $(n=m+m_1, m+m_1-1)$, where $q$ is a prime power. Furthermore, for $k\in\{3,4\}$, the symbol-pair weight distributions for these codes are determined by enumerating the number of polynomials with given roots.