Regular Circulant Matrices
Daniel Appel
TL;DR
This paper investigates the algebraic properties and group orders of regular circulant matrices over finite fields and residue rings, providing formulas and initial structural insights.
Contribution
It offers formulas for the order of regular circulant matrix groups and initiates exploration of their algebraic structure.
Findings
Derived formulas for group orders over finite fields and residue rings
Provided initial structural analysis of these matrix groups
Extended understanding of circulant matrices in algebraic contexts
Abstract
We consider the groups of regular circulant matrices over finite fields and integer residue class rings. In both cases we present a formula for the order of these groups. We also make a first step towards finding the algebraic structure of them.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Finite Group Theory Research