arXiv:2601.00435 · v3

On the burst-covering radius of binary cyclic codes

首次提交 2026-01-02 02:58

版本更新 2026-10-28 06:21

雷达观测 2026-10-30 10:23

摘要

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 bound on pattern frequencies in LFSR sequences, and using this tool, we 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.

作者备注：17 pages