Let T n (x, a) ʦ 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).
Factorization of Polynomials over Finite Fields and Characteristic Sequences
✍ Scribed by Harald Niederreiter; Rainer Göttfert
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 360 KB
- Volume
- 16
- Category
- Article
- ISSN
- 0747-7171
No coin nor oath required. For personal study only.
📜 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)Âf 2 (x){ g 1 (x p )Âg 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
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.
Let f and g be polynomials over some field, thought of as elements of the ring of one-sided Laurent series, and suppose that deg f<deg g. The quotient fÂg is badly approximable if all the partial quotients of the continued fraction expansion of fÂg have degree 1. We investigate the set of polynomial