{"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/modified-euclidean-algorithms-for-decoding","title":"Modified Euclidean Algorithms for Decoding Reed-Solomon Codes","arxiv_id":"0906.3778","date":"2009-06-22","proceeding":null,"authors":["Dilip V. Sarwate","Zhiyuan Yan"],"abstract":"The extended Euclidean algorithm (EEA) for polynomial greatest common divisors is commonly used in solving the key equation in the decoding of Reed-Solomon (RS) codes, and more generally in BCH decoding. For this particular application, the iterations in the EEA are stopped when the degree of the remainder polynomial falls below a threshold. While determining the degree of a polynomial is a simple task for human beings, hardware implementation of this stopping rule is more complicated. This paper describes a modified version of the EEA that is specifically adapted to the RS decoding problem. This modified algorithm requires no degree computation or comparison to a threshold, and it uses a fixed number of iterations. Another advantage of this modified version is in its application to the errors-and-erasures decoding problem for RS codes where significant hardware savings can be achieved via seamless computation.","url_abs":"http://arxiv.org/abs/0906.3778v1","url_pdf":"http://arxiv.org/pdf/0906.3778v1.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":"modified-euclidean-algorithms-for-decoding","repo_url":"https://github.com/pooruse/reed_solomon","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}