In this talk we will introduce burst-covering codes. The motivation behind their definition is twofold: they fill in a gap in the current literature, being the natural analogue to burst-error-correcting codes in a covering context, and they have potential applications to address locality issues in linear database queries. 

We will show some general bounds connecting the parameters of a code to its burst-covering radius. Then, we will focus on the study of binary cyclic codes, and we will show how computing their burst-covering radius is connected to the problem of counting patterns in linear-feedback shift-register (LFSR) sequences. For the case of BCH and Melas codes, classical results in this area are not strong enough, and thus we prove a new bound on pattern frequencies in LFSRs which is of independent interest. Finally, we will present a bound on the critical exponent of linear cyclic codes based on the burst-covering radius, improving on Kung’s bound.

This is joint work with Moshe Schwartz.

Arxiv: https://arxiv.org/abs/2601.00435