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The Distribution of Irreducible Polynomials in Fq[t]

✍ Scribed by Chih-Nung Hsu

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
530 KB
Volume
61
Category
Article
ISSN
0022-314X

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✦ Synopsis

The purpose of this article is to get effective information about the following two problems: (1) Making a polynomial irreducible by changing coefficients of lower degree terms. (2) Existence of irreducibles of low degree in a given arithmetic progression in polynomial ring over finite field.

πŸ“œ SIMILAR VOLUMES

Polynomial Distribution and Sequences of
Polynomial Distribution and Sequences of Irreducible Polynomials over Finite Fields
✍ Wun-Seng Chou; Stephen D Cohen πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 153 KB

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)Γ‚f 2 (x){ g 1 (x p )Γ‚g 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