2015/01/29 by H. M. de Oliveira, de Oliveira, H. M., Ricardo M. Campello de Souza +2
Computer Science · Mathematics · #Cellular Automata and Applications #Chaos-based Image/Signal Encryption #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #math.NT
paper · pdf · doi:10.48550/arxiv.1501.07502
6 pages, 1 figure. Conference: XVII Simposio Brasileiro de Telecomunicacoes, 1999, Vila Velha, ES, Brazil. (pp.472-477)
arxiv created 2015/01/29 · openalex publication_date 2015/01/29 · arxiv updated 2015/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.