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

Licence document URL: http://repositori.urv.cat/ca/proteccio-de-dades/

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

Article's DOI: 10.3390/sym11111357

Entity: Universitat Rovira i Virgili

Journal publication year: 2019

Publication Type: Journal Publications