Construction of Cyclic and Constacyclic Codes for b-symbol Read Channels Meeting the Plotkin-like Bound

TL;DR

This paper introduces a new bound for b-symbol read channels and constructs cyclic and constacyclic codes that meet this Plotkin-like bound, advancing coding theory for high-density data storage.

Contribution

It establishes a Plotkin-like bound for b-symbol read channels and provides constructions of codes that achieve this bound, extending previous work on MDS codes.

Findings

Established a Plotkin-like bound for b-symbol read channels

Constructed cyclic and constacyclic codes meeting the bound

Extended the theory of MDS codes for high-density storage applications

Abstract

The symbol-pair codes over finite fields have been raised for symbol-pair read channels and motivated by application of high-density data storage technologies [1, 2]. Their generalization is the code for b-symbol read channels (b > 2). Many MDS codes for b-symbol read channels have been constructed which meet the Singleton-like bound ([3, 4, 10] for b = 2 and [11] for b > 2). In this paper we show the Plotkin-like bound and present a construction on irreducible cyclic codes and constacyclic codes meeting the Plotkin-like bound.