Matrix powers over finite fields

Powers in finite fields

There are lots of results on the “random-like” behaviour of square elements in finite fields. For example, they can be used in combinatorial constructions and algorithms, as their properties somehow “imitate” a random distribution. In this paper we investigate the more general question concerning the behaviour of d-th powers in finite fields (where d is a fixed value). Surprisingly, they are di...

Matrix Theory over Finite Fields : A Survey

Recognizing finite matrix groups over infinite fields

Article history: Received 12 January 2012 Accepted 10 April 2012 Available online 15 June 2012

Random Matrix Theory over Finite Fields

The first part of this paper surveys generating functions methods in the study of random matrices over finite fields, explaining how they arose from theoretical need. Then we describe a probabilistic picture of conjugacy classes of the finite classical groups. Connections are made with symmetric function theory, Markov chains, Rogers-Ramanujan type identities, potential theory, and various meas...

Classical Wavelet Transforms over Finite Fields

This article introduces a systematic study for computational aspects of classical wavelet transforms over finite fields using tools from computational harmonic analysis and also theoretical linear algebra. We present a concrete formulation for the Frobenius norm of the classical wavelet transforms over finite fields. It is shown that each vector defined over a finite field can be represented as...