A symmetric matrix equation over a finite field
β Scribed by John H. Hodges
- Publisher
- John Wiley and Sons
- Year
- 1965
- Tongue
- English
- Weight
- 382 KB
- Volume
- 30
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
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.
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
It has been known for some time that every polynomial with coefficients from a finite field is the minimum polynomial of a symmetric matrix with entries from the same field. What have remained unknown, however, are the possible sizes for the symmetric matrices with a specified minimum polynomial and