📝 SummarXiv

Abstract

We investigate the problem of encoding data into an $(n, t)$-break-resilient code ($(n, t)$-BRC), i.e., a collections of sequences of length~$n$ from which the original data can be reconstructed even if they are adversarially broken at up to~$t$ arbitrary positions. We establish lower bounds on the redundancy of any $(n, t)$-BRC and present code constructions that meet these bounds up to asymptotically negligible terms. Interestingly, this problem shares similarities with the recently studied torn paper channel, which has emerged in the context of DNA data storage.