Adversarial Torn-paper Codes

We study the adversarial torn-paper channel. This problem is motivated by applications in DNA data storage where strands that carry information may break into smaller pieces which are received out of order. Our model extends previously researched probabilistic setting to worst-case. develop code constructions for any parameters channel non-vanishing asymptotic rate possible and show our achieve asymptotically optimal while allowing efficient encoding decoding. Finally, we extend results related settings included multi-strand storage, presence substitution errors, or incomplete coverage.