一类带有多项式迹形式的Semi-Bent函数的推广
A Generalization of One Class of Semi-Bent Functions with Polynomial Trace Form

作者: 陈 浩 * , 曹喜望 :南京航空航天大学理学院;

关键词: 布尔函数Semi-Bent函数Walsh-Hadamard转换Kloosterman和Cubic和Boolean Functions Semi-Bent Functions Walsh-Hadamard Transformation Kloosterman Sums Cubic Sums

摘要:
本文的主要是对一类已知的semi-Bent函数作进一步的推广。首先,我们来定义下列两个位于有限域上的具有多项式迹形式的布尔函数
,其中n=2m且m为奇数,r是一个正整数且。在文献[1]中,S. Mesnager已经讨论了当r=3或者 时,函数可能成为semi-Bent的情形。在本文中,我们将取消对的任何的限制条件,进一步的讨论函数成为semi-Bent函数的条件。在推广结论的过程中,我们要借助于Kloosterman和以及Cubic和这两样工具。

Abstract:
This paper is devoted to generalize a class of semi-Bent functions with even number of variables on the finite filed . We define the functions

and , where  n=2m with m odd, r is a positive integer and ,and . In the paper [1], S. Mesnagerhas discussed whether could be semi-bent function under the situations r=3 and . In this paper, we will give a further investigation on the function by removing the restrictions on r. We need to note that Kloosterman sums and cubic sums are essential to this paper.

文章引用: 陈 浩 , 曹喜望 (2013) 一类带有多项式迹形式的Semi-Bent函数的推广。 理论数学, 3, 120-125. doi: 10.12677/PM.2013.32019

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