On the Burst-Covering Radius of Binary Cyclic Codes

We define and study burst-covering codes. We provide some general bounds connecting the code parameters 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. 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.