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arXiv · 1501.07502

Introducing an Analysis in Finite Fields

H. M. de Oliveira·R. M. Campello de Souza
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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.

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H. M. de Oliveira, R. M. Campello de Souza. 2015-01-29. Introducing an Analysis in Finite Fields. https://arxiv.org/abs/1501.07502

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