Autor según el artículo: Bras-Amoros, Maria; O'Sullivan, Michael E.;
Departamento: Enginyeria Informàtica i Matemàtiques
e-ISSN: 2073-8994
Autor/es de la URV: Bras Amoros, Maria
Palabras clave: Sugiyama et al. algorithm Reed-solomon codes Key equation Euclidean algorithm Equivalence Berlekamp-massey algorithm
Resumen: 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.
Áreas temáticas: 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
Acceso a la licencia de uso: https://creativecommons.org/licenses/by/3.0/es/
ISSN: 20738994
Direcció de correo del autor: maria.bras@urv.cat
Identificador del autor: 0000-0002-3481-004X
Fecha de alta del registro: 2023-07-31
Volumen de revista: 11
Versión del articulo depositado: info:eu-repo/semantics/publishedVersion
Enlace a la fuente original: https://www.mdpi.com/2073-8994/11/11/1357
Referencia al articulo segun fuente origial: Symmetry-Basel. 11 (11):
Referencia de l'ítem segons les normes 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
URL Documento de licencia: https://repositori.urv.cat/ca/proteccio-de-dades/
DOI del artículo: 10.3390/sym11111357
Entidad: Universitat Rovira i Virgili
Año de publicación de la revista: 2019
Tipo de publicación: Journal Publications
Repositori URV