On PS Bent Functions

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 2^n/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