On the construction of bent functions of $n+2$ variables from bent functions of $n$ variables

A Construction of Bent Functions of n+2 Variables from a Bent Function of n Variables and Its Cyclic Shifts

“…In Section 4, we present the necessary results to count the number of bent functions we can construct based on the method dealt with in Section 3. Finally, in Section 5, we show that our construction generates bent functions which are not Rothaus or Maiorana-McFarland type (see, e.g., [29,37]); we also show that the construction introduced in this paper is basically different from the construction introduced in [22] and we compute the number of bent functions we can obtain using one construction but not by the other one. In addition, we summarize the number of bent functions obtained by the different methods here considered.…”

“…In [22] we introduced the following construction of bent functions of +2 variables using bent functions of variables and the minterms of two variables.…”

“…In addition, we also establish [22,Theorem 3] that the number of different bent functions of + 2 variables we can construct using the previous theorem is…”

“…Nevertheless, the classical concept of minterm, which, by the way, is directly related to the implementation of logic circuits and its complexity, has not been frequently applied (see [22]). This paper purports to practically generate bent functions using the representation of Boolean functions as a sum of minterms.…”

On the construction of new bent functions from the max-weight and min-weight functions of old bent functions

“…The following result, which proof can be found in [11], provides four minterms of n + 2 variables from one minterm of n variables.…”