An n?pm random access code (RAC) is an encoding of xmlns:mml="http://www.w3.org/1998/Math/MathML">n bits into xmlns:mml="http://www.w3.org/1998/Math/MathML">m such t...

In this paper a new approach for designing Boolean functions that satisfy the Strict Avalanche Criterion (SAC) is presented. The advantage of the suggested approach is the simplicity of its realization and the significant greater number of the generated functions compared to the known methods. The formalized procedure for construction of nonbalanced and balanced SAC-functions is described in de...

The largest Hamming distance between a Boolean function in $n$ variables and the set of all affine Boolean functions in $n$ variables is known as the covering radius $\rho_n$ of the $[2^n,n+1]$ Reed-Muller code. This number determines how well Boolean functions can be approximated by linear Boolean functions. We prove that \[ \lim_{n\to\infty}2^{n/2}-\rho_n/2^{n/2-1}=1, \] which resolves a conj...