On fundamental sets over a finite field
type: Item
instance of: scholarly article
title: On fundamental sets over a finite field
zbMATH Open document ID: 0575.12015
DOI: 10.1155/S0161171285000394
author: Yousef Abbas
author: Joseph J. Liang
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/45974
review text: Let \(\alpha \in GF(p^ n)\). The authors define \(A_{\alpha}=\{\alpha,\alpha +1,...,\alpha +p-1\}\), \({}^*A_{\alpha}=\cup^{p-1}_{l=1}A_{l\alpha}\), \(\bar A_{\alpha}=\cup^{n-1}_{l=0}{}^*A_{\alpha}^{p^ l}\), and \(\alpha\sim\beta\) iff \(\bar A_{\alpha}=\bar A_{\beta}\). The equivalence relation \(\sim\) partitions the field \(GF(p^ n)\) into fundamental classes. To study the fundamental classes the authors discuss the solutions of the equations of the form \(x^{p^ m}=ax+b\). In the last section they investigate the number of fundamental classes for some finite fields.
Mathematics Subject Classification ID: 11T99
Mathematics Subject Classification ID: 11T06
Mathematics Subject Classification ID: 11T55
zbMATH DE Number: 3918502
zbMATH Keywords: fundamental sets
zbMATH Keywords: partitions
zbMATH Keywords: fundamental classes
zbMATH Keywords: finite fields
MaRDI profile type: Publication
OpenAlex ID: W2060069122
description: scientific article; zbMATH DE number 3918502