The Factorization of Dickson Polynomials over Finite Fields
β Scribed by Wun-Seng Chou
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 257 KB
- Volume
- 3
- Category
- Article
- ISSN
- 1071-5797
No coin nor oath required. For personal study only.
β¦ Synopsis
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).
π SIMILAR VOLUMES
We exhibit a deterministic algorithm for factoring polynomials in one variable over "nite "elds. It is e$cient only if a positive integer k is known for which I (p) is built up from small prime factors; here I denotes the kth cyclotomic polynomial, and p is the characteristic of the "eld. In the cas
This survey reviews several algorithms for the factorization of univariate polynomials over finite fields. We emphasize the main ideas of the methods and provide an up-to-date bibliography of the problem.
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.