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.

Skew-tolerant Gray codes are Gray codes in which changes in consecutive codewords occur in adjacent positions. We present the first constructions of asymptotically non-vanishing skew-tolerant Gray codes, offering an exponential improvement over previous work.

Skew-tolerant Gray codes are Gray codes in which changes in consecutive codewords occur in adjacent positions. We present the first construction of asymptotically non-vanishing skew-tolerant Gray codes, offering an exponential improvement over previous work. We also provide linear-time encoding and decoding algorithms for our codes. Finally, we extend the definition to non-binary alphabets, and provide constructions of completem-ary skew-tolerant Gray codes for every basem⩾ 3.