Author, as appears in the article.: Bras-Amorós M

Department: Enginyeria Informàtica i Matemàtiques

URV's Author/s: Bras Amoros, Maria

Abstract: Because of their importance in applications and their quite simple definition, Reed-Solomon codes can be explained in any introductory course on coding theory. However, decoding algorithms for Reed-Solomon codes are far from being simple and it is difficult to fit them in introductory courses for undergraduates. We introduce a new decoding approach, in a self-contained presentation, which we think may be appropriate for introducing error correction of Reed-Solomon codes to nonexperts. In particular, we interpret Reed-Solomon codes by means of the degree of the interpolation polynomial of the code words and from this derive a decoding algorithm. Compared to the classical algorithms, our algorithm appears to arise more naturally from definitions and to be easier to understand. It is related to the Peterson-Gorenstein-Zierler algorithm (see [10 Gorenstein, D., Zierler, N. (1961). A class of error-correcting codes in pm symbols. J. Soc. Indust. Appl. Math. 9: 207-214. [Google Scholar]] and [20 Peterson, W. W. (1960). Encoding and error-correction procedures for the Bose-Chaudhuri codes.

Thematic Areas: Mathematics (miscellaneous) Mathematics (all) Mathematics Matemática / probabilidade e estatística General mathematics Ciência da computação

licence for use: https://creativecommons.org/licenses/by/3.0/es/

Author's mail: maria.bras@urv.cat

Author identifier: 0000-0002-3481-004X

Record's date: 2023-02-18

Papper version: info:eu-repo/semantics/acceptedVersion

Link to the original source: https://www.tandfonline.com/doi/abs/10.1080/00029890.2018.1420333?journalCode=uamm20

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

Papper original source: American Mathematical Monthly. 125 (4): 320-338

APA: Bras-Amorós M (2018). A Decoding Approach to Reed-Solomon Codes from Their Definition. American Mathematical Monthly, 125(4), 320-338. DOI: 10.1080/00029890.2018.1420333

Article's DOI: 10.1080/00029890.2018.1420333

Entity: Universitat Rovira i Virgili

Journal publication year: 2018

Publication Type: Journal Publications