24,627 research outputs found
Elliptic periods for finite fields
We construct two new families of basis for finite field extensions. Basis in
the first family, the so-called elliptic basis, are not quite normal basis, but
they allow very fast Frobenius exponentiation while preserving sparse
multiplication formulas. Basis in the second family, the so-called normal
elliptic basis are normal basis and allow fast (quasi linear) arithmetic. We
prove that all extensions admit models of this kind
Chebyshev Action on Finite Fields
Given a polynomial f and a finite field F one can construct a directed graph
where the vertices are the values in the finite field, and emanating from each
vertex is an edge joining the vertex to its image under f. When f is a
Chebyshev polynomial of prime degree, the graphs display an unusual degree of
symmetry. In this paper we provide a complete description of these graphs, and
also provide some examples of how these graphs can be used to determine the
decomposition of primes in certain field extensions
Counting curves over finite fields
This is a survey on recent results on counting of curves over finite fields.
It reviews various results on the maximum number of points on a curve of genus
g over a finite field of cardinality q, but the main emphasis is on results on
the Euler characteristic of the cohomology of local systems on moduli spaces of
curves of low genus and its implications for modular forms.Comment: 25 pages, to appear in Finite Fields and their Application
Constacyclic Codes over Finite Fields
An equivalence relation called isometry is introduced to classify
constacyclic codes over a finite field; the polynomial generators of
constacyclic codes of length are characterized, where is the
characteristic of the finite field and is a prime different from
- …