On PS Bent Functions

Abstract

In this paper, properties and constructions of the class of PS bent functions are considered, which is one special class of bent functions having good algebraic structure and is useful for studying the general structure of bent functions. It is an open problem to characterize the algebraic normal forms of PS bent functions. To construct the bent functions of class PS, we must divide F2 n into 2n/2+1 subspace of dimension n/2 firstly. In this paper, we will study this problem and give one generalized method to divide F2 n, so we can construct PS bent functions easily. Also the algebraic normal forms of PS bent functions are provided