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.