Abstract
Reed-Solomon codes are indeed an elegant illustration of a very practical application of abstract algebra. An interesting discovery was the fact that Euclid’s algorithm for finding greatest common divisors of polynomials, could be used for decoding these codes. In this article we explain this connection.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Suggested Reading
Elwyn Berlekamp, Algebraic Coding Theory, McGraw-Hill, New York, 1968.
Y Sugiyama, M Kasahara, S Hirasawa and T Namekawa, A method for solving key equation for decoding Goppa codes, Information and Control, Vol.27, pp. 87–99, 1975.
Priti Shankar, Error Correcting Codes: The Reed-Solomon Codes, Resonance, Vol.2, No.3, pp.33–47, 1997.
R J McEliece, The Theory of Information and Coding, Encyclopedia of Mathematics and its Applications, Addison Wesley, 1977.
Author information
Authors and Affiliations
Corresponding author
Additional information
Priti Shankar is with the Department of Computer Science and Automation at the Indian Institute of Science, Bangalore. Her interests are in theoretical computer science and error correcting codes.
Rights and permissions
About this article
Cite this article
Shankar, P. Decoding Reed-Solomon codes using Euclid’s algorithm. Reson 12, 37–51 (2007). https://doi.org/10.1007/s12045-007-0037-y
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12045-007-0037-y