On the burst-covering radius of binary cyclic codes

TL;DR

This paper introduces the concept of burst-covering codes, establishes bounds on their parameters, and specifically analyzes the burst-covering radius of cyclic codes using LFSR sequences, with applications to BCH and Melas codes.

Contribution

It provides new bounds on the burst-covering radius of cyclic codes and introduces an efficient algorithm for burst-covering, advancing coding theory research.

Findings

Derived bounds on burst-covering radius for cyclic codes

Proved a new pattern frequency bound in LFSR sequences for BCH codes

Presented an efficient burst-covering algorithm for cyclic codes

Abstract

We define and study burst-covering codes. We provide some general bounds connecting the parameters of a code with its burst-covering radius. We then provide stronger bounds on the burst-covering radius of cyclic codes, by employing linear-feedback shift-register (LFSR) sequences. For the case of BCH codes we prove a new bound on pattern frequencies in LFSR sequences, which is of independent interest. Using this tool, we can bound the burst-covering radius of binary primitive BCH codes and Melas codes. We then present an efficient burst-covering algorithm for cyclic codes. Finally, we present a bound on the critical exponent of cyclic codes based on the burst-covering radius.