On the burst-covering radius of binary cyclic codes
Information Theory
2026-04-09 v2 math.IT
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.
Keywords
Cite
@article{arxiv.2601.00435,
title = {On the burst-covering radius of binary cyclic codes},
author = {Gabriel Sac Himelfarb and Moshe Schwartz},
journal= {arXiv preprint arXiv:2601.00435},
year = {2026}
}
Comments
16 pages