Autor segons l'article: Bras-Amoros, Maria; O'Sullivan, Michael E.;
Departament: Enginyeria Informàtica i Matemàtiques
e-ISSN: 2073-8994
Autor/s de la URV: Bras Amoros, Maria
Paraules clau: Sugiyama et al. algorithm Reed-solomon codes Key equation Euclidean algorithm Equivalence Berlekamp-massey algorithm
Resum: 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.
Àrees temàtiques: 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
Accès a la llicència d'ús: https://creativecommons.org/licenses/by/3.0/es/
ISSN: 20738994
Adreça de correu electrònic de l'autor: maria.bras@urv.cat
Identificador de l'autor: 0000-0002-3481-004X
Data d'alta del registre: 2023-07-31
Volum de revista: 11
Versió de l'article dipositat: info:eu-repo/semantics/publishedVersion
Enllaç font original: https://www.mdpi.com/2073-8994/11/11/1357
Referència a l'article segons font original: Symmetry-Basel. 11 (11):
Referència 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 Document de llicència: https://repositori.urv.cat/ca/proteccio-de-dades/
DOI de l'article: 10.3390/sym11111357
Entitat: Universitat Rovira i Virgili
Any de publicació de la revista: 2019
Tipus de publicació: Journal Publications
Repositori URV