﻿ 一类带有多项式迹形式的Semi-Bent函数的推广

# 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

，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.

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