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
Number of Zeros of Diagonal Polynomials over Finite Fields
β 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.
π SIMILAR VOLUMES
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.
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.
By using results of coding theory, we give results on the number of solutions of some systems of diagonal equations over finite fields.
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
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).