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.
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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.
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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.
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Shankar, P. Decoding Reed-Solomon codes using Euclid’s algorithm. Reson 12, 37–51 (2007). https://doi.org/10.1007/s12045-007-0037-y
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DOI: https://doi.org/10.1007/s12045-007-0037-y