On the equation x2l+1+x+a=0 over GF(2k)

被引：35

作者：

Helleseth, Tor ^{[1
]}

Kholosha, Alexander ^{[1
]}

机构：

[1] Univ Bergen, Selmer Ctr, Dept Informat, N-5020 Bergen, Norway

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2008年 / 14卷 / 01期

关键词：

equation over finite field; permutation polynomial;

D O I：

10.1016/j.ffa.2007.09.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the polynomials P-a(x) =x(2'+1) + x + a with a is an element of GF(2(k)) are studied. Some new criteria for the number of zeros of P-a (x) in GF(2(k)) are proved. In particular, a criterion for P-a (x) to have exactly one zero in GF(2(k)) when gcd(l, k) = 1 is formulated in terms of the values of polynomials introduced by Dobbertin. In the case when there is a unique zero, this root is calculated explicitly. (c) 2007 Elsevier Inc. All rights reserved.

引用

页码：159 / 176

页数：18

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