# Boolean functions

## Three classes of balanced vectorial semi-bent functions

Semi-bent functions play an important role in symmetric ciphers and sequence designs. So far, there are few studies related to the construction of vectorial semi-bent functions even though lots of work has been done on single-output semi-bent …

## Constructions of balanced Boolean functions on even number of variables with maximum absolute value in autocorrelation spectra $<2^{{n/2}^{\star}}$

The autocorrelation properties of Boolean functions are closely related to the Shannon’s concept of diffusion and can be accompanied with other cryptographic criteria (such as high nonlinearity and algebraic degree) for ensuring an overall robustness …

## Infinite classes of generalised complete permutations

In Pasalic et al. (2016) a construction allowing for high levels of modification was presented. It can be used to construct several important combinatorial structures, among them are examples of complete permutations. Here the method is used to …

## Proving the conjecture of O’Donnell in certain cases and disproving its general validity

For a function $f:\\{−1,1\\}^n\\to \\{−1,1\\}$ the relationship between the sum of its linear Fourier coefficients $\\hat{f}(i)$ (defined by $\\hat{f}(i)≔\\frac{1}{2^n}\\sum_{x\in \\{−1,1\\}^n} f(x)x_i$ for $i=1,2,\\ldots,n$ and …