Fast Construction of Irreducible Polynomials over Finite Fields
โ Scribed by Victor Shoup
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 657 KB
- Volume
- 17
- Category
- Article
- ISSN
- 0747-7171
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Let k=GF(q) be the finite field of order q. Let f 1 (x), f 2 (x) # k[x] be monic relatively prime polynomials satisfying n=deg f 1 >deg f 2 0 and f 1 (x)รf 2 (x){ g 1 (x p )รg 2 (x p ) for any g 1 (x), g 2 (x) # k[x]. Write Q(x)= f 1 (x)+tf 2 (x) and let K be the splitting field of Q(x) over k(t). L
Counting irreducible factors of polynomials over a finite field, Discrete Mathematics, 112 (1993) 103-l 18. Let F,[X] denote a polynomial ring in an indeterminate X over a finite field IF,. Exact formulae are derived for (i) the number of polynomials of degree n in F,[X] with a specified number of i
A recently discovered family of indecomposable polynomials of nonprime power degree over \(\mathbb{F}_{2}\) (which include a class of exceptional polynomials) is set against the background of the classical families and their monodromy groups are obtained without recourse to the classification of fin
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