Author, as appears in the article.: Bras-Amoros, Maria; O'Sullivan, Michael E.;
Department: Enginyeria Informàtica i Matemàtiques
e-ISSN: 2073-8994
URV's Author/s: Bras Amoros, Maria
Keywords: Sugiyama et al. algorithm Reed-solomon codes Key equation Euclidean algorithm Equivalence Berlekamp-massey algorithm
Abstract: This paper presents a new way to view the key equation for decoding Reed-Solomon codes that unites the two algorithms used in solving it-the Berlekamp-Massey algorithm and the Euclidean algorithm. A new key equation for Reed-Solomon codes is derived for simultaneous errors and erasures decoding using the symmetry between polynomials and their reciprocals as well as the symmetries between dual and primal codes. The new key equation is simpler since it involves only degree bounds rather than modular computations. We show how to solve it using the Euclidean algorithm. We then show that by reorganizing the Euclidean algorithm applied to the new key equation we obtain the Berlekamp-Massey algorithm.
Thematic Areas: Visual arts and performing arts Physics and astronomy (miscellaneous) Multidisciplinary sciences Modeling and simulation Mathematics, interdisciplinary applications Mathematics (miscellaneous) Mathematics (all) Matemática / probabilidade e estatística General mathematics Engineering (miscellaneous) Computer science (miscellaneous) Ciência da computação Chemistry (miscellaneous) Arts and humanities (miscellaneous) Architecture Applied mathematics
licence for use: https://creativecommons.org/licenses/by/3.0/es/
ISSN: 20738994
Author's mail: maria.bras@urv.cat
Author identifier: 0000-0002-3481-004X
Record's date: 2023-07-31
Journal volume: 11
Papper version: info:eu-repo/semantics/publishedVersion
Link to the original source: https://www.mdpi.com/2073-8994/11/11/1357
Papper original source: Symmetry-Basel. 11 (11):
APA: Bras-Amoros, Maria; O'Sullivan, Michael E.; (2019). The Symmetric Key Equation for Reed-Solomon Codes and a New Perspective on the Berlekamp-Massey Algorithm. Symmetry-Basel, 11(11), -. DOI: 10.3390/sym11111357
Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
Article's DOI: 10.3390/sym11111357
Entity: Universitat Rovira i Virgili
Journal publication year: 2019
Publication Type: Journal Publications
Repositori URV