On group automata over finite fields

On group automata over finite fields

We investigate the structure of incidence rings of group automata over finite fields. One of the major tools used in research on the structure of ring constructions is the Jacobson radical. Our main theorem gives a complete description of the Jacobson radicals of incidence rings of (possibly nondeterministic) group automata over finite fields in the important special case where the input group ...

The Automorphism Group over Finite Fields

It is shown that the invertible polynomial maps over a finite field Fq, if looked at as bijections Fq −→ Fq , give all possible bijections in case q = 2, or q = p where p > 2. In case q = 2 where r > 1 it is shown that the tame subgroup of the invertible polynomial maps give only the even bijections, i.e. only half the bijections. As a consequence it is shown that a set S ⊂ Fq can be a zero set...

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...

Classical wavelet systems over finite fields

This article presents an analytic approach to study admissibility conditions related to classical full wavelet systems over finite fields using tools from computational harmonic analysis and theoretical linear algebra. It is shown that for a large class of non-zero window signals (wavelets), the generated classical full wavelet systems constitute a frame whose canonical dual are classical full ...

Finding the Group Structure of Elliptic Curves over Finite Fields