The number of irreducible polynomials of degree n over Fq with given trace and constant terms

被引：10

作者：

Koma, B. Omidi ^{[1
]}

Panario, D. ^{[1
]}

Wang, Q. ^{[1
]}

机构：

[1] Carleton Univ, Sch Math & Stat, Ottawa, ON K1S 5B6, Canada

来源：

DISCRETE MATHEMATICS | 2010年 / 310卷 / 08期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Finite fields; Irreducible polynomials; Trace and constant terms; PRESCRIBED COEFFICIENTS; ELLIPTIC-CURVES; FINITE-FIELDS; GF(2);

D O I：

10.1016/j.disc.2009.12.006

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the number N-gamma (n, c, q) of irreducible polynomials of degree n over F-q where the trace gamma and the constant term c are given. Under certain conditions on n and q, we obtain bounds on the maximum of N-gamma (n, c, q) varying c and gamma. We show with concrete examples how our results improve the previously known bounds. In addition, we improve upper and lower bounds of any N-gamma(n, c, q) when n = a(q - 1) for a nonzero constant term c and a nonzero trace gamma. As a byproduct, we give a simple and explicit formula for the number N(n, c. q) of irreducible polynomials over F-q of degree n = q-1 with a prescribed primitive constant term c. (C) 2009 Elsevier B.V. All rights reserved.

引用

页码：1282 / 1292

页数：11

共 13 条

[1] A THEOREM OF DICKSON ON IRREDUCIBLE POLYNOMIALS [J].