A new class of MDS symbol-pair codes
Canze Zhu, Qunying Liao

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 and , we construct a class of -ary MDS symbol-pair codes with dimension and length , where is a prime power. Furthermore, for , the symbol-pair weight distributions for these codes are determined by enumerating the number of polynomials with given roots.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Cellular Automata and Applications
