New constructions and lower bound of number of self-dual bent functions

Abstract

The paper considers maximally non-linear Boolean functions of even number of variables - bent functions. These functions have a number applications in coding theory and cryptography. For each bent function, the dual to it bent functions. A bent function is called self-dual if it coincides with its dual. Characteristic vectors of self-dual bent functions are eigenvectors of the matrix Sylvester-Hadamard, which has applications in combinatorics, theory signals and quantum computing. The paper proposes a number of new iterative constructions of self-dual bent functions of n variables, in within which the vectors of values of bent functions from n-4 variables. Based on the analysis of sets of functions generated by data constructions, as well as previously known iterative constructions, a new iterative lower bound for the number of self-dual bent functions.