Introducing an Analysis in Finite Fields
Number Theory
2015-01-30 v1
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.
Keywords
Cite
@article{arxiv.1501.07502,
title = {Introducing an Analysis in Finite Fields},
author = {H. M. de Oliveira and R. M. Campello de Souza},
journal= {arXiv preprint arXiv:1501.07502},
year = {2015}
}
Comments
6 pages, 1 figure. Conference: XVII Simposio Brasileiro de Telecomunicacoes, 1999, Vila Velha, ES, Brazil. (pp.472-477)