Elliptic curves and explicit enumeration of irreducible polynomials with two coefficients prescribed

被引：14

作者：

Moisio, Marko ^{[2
]}

Ranto, Kalle ^{[1
]}

机构：

[1] Univ Turku, Dept Math, FIN-20014 Turku, Finland

[2] Univ Vaasa, Dept Math & Stat, FIN-65101 Vaasa, Finland

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2008年 / 14卷 / 03期

基金：

芬兰科学院;

关键词：

Kloosterman sum; exponential sum function field; rational place; Dickson polynomial; BCH coded; Melas code;

D O I：

10.1016/j.ffa.2008.01.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let F-q be a finite field of characteristic p = 2, 3. We give the number of irreducible polynomials x(m) + a(m-1) x(m-1) + ... + a(0) F-q [x] with a(m-1) and a(m-3) prescribed for any given in if p = 2, and with a(m-1) and a(1) prescribed for m = 1,.... 10 if p = 2, 3. In the latter case an enumeration formula, applicable also if m > 10, is given, but it is explicit only up to the evaluation of certain Kronecker class numbers. (c) 2008 Elsevier Inc. All rights reserved.

引用

页码：798 / 815

页数：18

共 16 条

[11]

Niederreiter H., 1990, APPL ALGEBR ENG COMM, V1, P119

[12] HECKE OPERATORS AND THE WEIGHT DISTRIBUTIONS OF CERTAIN CODES [J].