{"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/optimal-codes-correcting-a-single-indel-edit","title":"Optimal Codes Correcting a Single Indel / Edit for DNA-Based Data Storage","arxiv_id":"1910.06501","date":"2019-10-15","proceeding":null,"authors":["Kui Cai","Yeow Meng Chee","Ryan Gabrys","Han Mao Kiah","Tuan Thanh Nguyen"],"abstract":"An indel refers to a single insertion or deletion, while an edit refers to a single insertion, deletion or substitution. In this paper, we investigate codes that combat either a single indel or a single edit and provide linear-time algorithms that encode binary messages into these codes of length n. Over the quaternary alphabet, we provide two linear-time encoders. One corrects a single edit with log n + O(log log n) redundancy bits, while the other corrects a single indel with log n + 2 redundant bits. These two encoders are order-optimal. The former encoder is the first known order-optimal encoder that corrects a single edit, while the latter encoder (that corrects a single indel) reduces the redundancy of the best known encoder of Tenengolts (1984) by at least four bits. Over the DNA alphabet, we impose an additional constraint: the GC-balanced constraint and require that exactly half of the symbols of any DNA codeword to be either C or G. In particular, via a modification of Knuth's balancing technique, we provide a linear-time map that translates binary messages into GC-balanced codewords and the resulting codebook is able to correct a single indel or a single edit. These are the first known constructions of GC-balanced codes that correct a single indel or a single edit.","url_abs":"https://arxiv.org/abs/1910.06501v1","url_pdf":"https://arxiv.org/pdf/1910.06501v1.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":"optimal-codes-correcting-a-single-indel-edit","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}