{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/codes-correcting-a-burst-of-deletions-or","title":"Codes Correcting a Burst of Deletions or Insertions","arxiv_id":"1602.06820","date":"2016-02-22","proceeding":null,"authors":["Clayton Schoeny","Antonia Wachter-Zeh","Ryan Gabrys","Eitan Yaakobi"],"abstract":"This paper studies codes that correct bursts of deletions. Namely, a code will be called a $b$-burst-deletion-correcting code if it can correct a deletion of any $b$ consecutive bits. While the lower bound on the redundancy of such codes was shown by Levenshtein to be asymptotically $\\log(n)+b-1$, the redundancy of the best code construction by Cheng et al. is $b(\\log (n/b+1))$. In this paper we close on this gap and provide codes with redundancy at most $\\log(n) + (b-1)\\log(\\log(n)) +b -\\log(b)$. We also derive a non-asymptotic upper bound on the size of $b$-burst-deletion-correcting codes and extend the burst deletion model to two more cases: 1) A deletion burst of at most $b$ consecutive bits and 2) A deletion burst of size at most $b$ (not necessarily consecutive). We extend our code construction for the first case and study the second case for $b=3,4$. The equivalent models for insertions are also studied and are shown to be equivalent to correcting the corresponding burst of deletions.","url_abs":"https://arxiv.org/abs/1602.06820v2","url_pdf":"https://arxiv.org/pdf/1602.06820v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"codes-correcting-a-burst-of-deletions-or","repo_url":"https://github.com/dtch1997/single-edit-correcting-code","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}