𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Number of Zeros of Diagonal Polynomials over Finite Fields

✍ Scribed by Ren Debin; Sun Qi; Yuan Pingzhi


Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
98 KB
Volume
7
Category
Article
ISSN
1071-5797

No coin nor oath required. For personal study only.


πŸ“œ SIMILAR VOLUMES


On the Number of Solutions of Diagonal E
✍ Qi Sun; Ping-Zhi Yuan πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 181 KB

In this paper, we give a reduction theorem for the number of solutions of any diagonal equation over a finite field. Using this reduction theorem and the theory of quadratic equations over a finite field, we also get an explicit formula for the number of solutions of a diagonal equation over a finit

A Class of Polynomials over Finite Field
✍ Arnaldo Garcia; Henning Stichtenoth πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 129 KB

Generalizing the norm and trace mappings for % O P /% O , we introduce an interesting class of polynomials over "nite "elds and study their properties. These polynomials are then used to construct curves over "nite "elds with many rational points.

Groups of Permutation Polynomials over F
✍ Richard M. Stafford πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 195 KB

Let F be a finite field. We apply a result of Thierry Berger (1996, Designs Codes Cryptography, 7, 215-221) to determine the structure of all groups of permutations on F generated by the permutations induced by the linear polynomials and any power map which induces a permutation on F.

Some Systems of Diagonal Equations over
✍ Jacques Wolfmann πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 254 KB

By using results of coding theory, we give results on the number of solutions of some systems of diagonal equations over finite fields.

Counting Polynomials with Zeros of Given
✍ Jean-FranΓ§ois Ragot πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 136 KB

We consider the set of polynomials in r indeterminates over a "nite "eld and with bounded degree. We give here a way to count the number of elements of some of its subsets, namely those sets de"ned by the multiplicities of their elements at some points of %P O . The number of polynomials having at l

The Factorization of Dickson Polynomials
✍ Wun-Seng Chou πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 257 KB

Let T n (x, a) Κ¦ GF(q)[x] be a Dickson polynomial over the finite field GF(q) of either the first kind or the second kind of degree n in the indeterminate x and with parameter a. We give a complete description of the factorization of T n (x, a) over GF(q).