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Efficient evaluations of polynomials over finite fields


Schipani, D; Elia, M; Rosenthal, J (2011). Efficient evaluations of polynomials over finite fields. In: IEEE. Proceedings of the 2011 Australian Communications Theory Workshop : the University of Melbourne, Melbourne, Australia, 31st January - 2nd February 2011. Piscataway, NJ, US: IEEE, 154-157.

Abstract

A method is described which allows to evaluate efficiently a polynomial in a (possibly trivial) extension of the finite field of its coefficients. Its complexity is shown to be lower than that of standard techniques when the degree of the polynomial is large with respect to the base field. Applications to the syndrome computation in the decoding of cyclic codes, Reed-Solomon codes in particular, are highlighted.

Abstract

A method is described which allows to evaluate efficiently a polynomial in a (possibly trivial) extension of the finite field of its coefficients. Its complexity is shown to be lower than that of standard techniques when the degree of the polynomial is large with respect to the base field. Applications to the syndrome computation in the decoding of cyclic codes, Reed-Solomon codes in particular, are highlighted.

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Additional indexing

Contributors:NICTA (Australia), IEEE Information Theory Society, CSIRO (Australia)
Item Type:Book Section, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2011
Deposited On:14 Jan 2012 18:34
Last Modified:07 Dec 2017 11:19
Publisher:IEEE
ISBN:978-1-4244-9714-0 (P)
Publisher DOI:https://doi.org/10.1109/AUSCTW.2011.5728754

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