Introducing an Analysis in Finite Fields
arXiv:1501.07502
Abstract
Looking forward to introducing an analysis in Galois Fields, discrete functions are considered (such as transcendental ones) and MacLaurin series are derived by Lagrange's Interpolation. A new derivative over finite fields is defined which is based on the Hasse Derivative and is referred to as negacyclic Hasse derivative. Finite field Taylor series and alpha-adic expansions over GF(p), p prime, are then considered. Applications to exponential and trigonometric functions are presented. Theses tools can be useful in areas such as coding theory and digital signal processing.
6 pages, 1 figure. Conference: XVII Simposio Brasileiro de Telecomunicacoes, 1999, Vila Velha, ES, Brazil. (pp.472-477)