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2019 Galois wavelet transforms over finite fields
Arash Ghaani Farashahi
Rocky Mountain J. Math. 49(1): 79-99 (2019). DOI: 10.1216/RMJ-2019-49-1-79

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.

Citation

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Arash Ghaani Farashahi. "Galois wavelet transforms over finite fields." Rocky Mountain J. Math. 49 (1) 79 - 99, 2019. https://doi.org/10.1216/RMJ-2019-49-1-79

Information

Published: 2019
First available in Project Euclid: 10 March 2019

zbMATH: 07036620
MathSciNet: MR3921868
Digital Object Identifier: 10.1216/RMJ-2019-49-1-79

Subjects:
Primary: 12E20 , ‎42C40
Secondary: 12F10 , 13B05 , 20G40 , 81R05

Keywords: finite field , Galois dilation operator , Galois wavelet group , Galois wavelet representation , Galois wavelet transform , periodic (finite size) data , prime integer

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.49 • No. 1 • 2019
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