Generalized k-linear equations over a finite field
β Scribed by Robert G. van Meter
- Publisher
- John Wiley and Sons
- Year
- 1972
- Tongue
- English
- Weight
- 196 KB
- Volume
- 53
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
β¦ Synopsis
X generalization of a theorem of A. D. PORTER on the number of solutions of the k-linear equation 2 ai n x , ~ = a over a finite field is given.
π SIMILAR VOLUMES
We get an explicit formula for the number of solutions of a diagonal equation over finite fields, under a certain natural restriction on the exponents.
In this paper, we obtain a su$cient condition for the diagonal equation to have only the trivial solution over "nite "elds. This result improves a theorem of Sun (J. Sichuan Normal ;niv. Nat. Sci. Ed. 26 (1989), 55}59) greatly and proves that the conjecture posed by Powell (J. Number ΒΉheory 18 (1984
By using results of coding theory, we give results on the number of solutions of some systems of diagonal equations over finite fields.