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David Alan Lingenbrink, Jr.

Picture of David Alan Lingenbrink, Jr..

Thesis

A New Subgroup Chain for the Finite Affine Group

Advisor
Michael E. Orrison
Second Reader(s)
Mohamed Omar

Abstract

The finite affine group is a matrix group whose entries come from a finite field. A natural subgroup consists of those matrices whose entries all come from a subfield instead. In this paper, I will introduce intermediate subgroups with entries from both the field and a subfield. I will also examine the representations of these intermediate subgroups as well as the branching diagram for the resulting subgroup chain. This will allow us to create a fast Fourier transform for the group that uses asymptotically fewer operations than the brute force algorithm.

Proposal

Fast Fourier Transforms using Field Extensions

Additional Materials

Poster