On codes for structured bursts

We introduce a technique for constructing codes for bursts of errors that have some known structure; for example bursts of length at most b and Hamming weight at most t. This technique is based on modifying existing codes for generic bursts by replacing a portion of their check matrix with a more efficient one, in light of the additional constraints on the burst. We illustrate this procedure by modifying the Fire, Burton and Gilbert codes to address bursts with maximum Hamming weight, bursts with solid errors, or bursts with internal "mini-bursts". We provide evidence that the redundancy of the codes we construct can be very good through examples, one of which is optimal within the class of cyclic codes.