On the burst-covering radius of binary cyclic codes
This work addresses error correction in coding theory, specifically for burst errors in cyclic codes, but it appears incremental as it builds on existing methods to derive new bounds and algorithms.
The paper tackles the problem of analyzing burst-covering codes by defining and studying their burst-covering radius, providing general and stronger bounds for cyclic codes using LFSR sequences, and proving a new bound for BCH codes that leads to specific bounds for binary primitive BCH and Melas codes, along with an efficient algorithm and a bound on critical exponent.
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.