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

URL Documento de licencia: http://repositori.urv.cat/ca/proteccio-de-dades/

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

DOI del artículo: 10.3390/sym11111357

Entidad: Universitat Rovira i Virgili

Año de publicación de la revista: 2019

Tipo de publicación: Journal Publications