Galois wavelet transforms over finite fields

Abstract

In this article, we introduce the abstract notion of Galois wavelet groups over finite fields as the finite group of Galois dilations, and translations. We then present a unified theoretical linear algebra approach to the theory of Galois wavelet transforms over finite fields. It is shown that each vector defined over a finite field can be represented as a finite coherent sum of Galois wavelet coefficients as well.