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
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 及 ，其中n=2m且m为奇数，r是一个正整数且，及 。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. 一类带有多项式迹形式的Semi-Bent函数的推广[J]. 理论数学, 2013, 3(2): 120-125. http://dx.doi.org/10.12677/PM.2013.32019

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