We give a new lower bound to the covering radius of the first order Reed–Muller code RM
(1, n), where n∈{9, 11, 13}. Equivalently, we present the n-variable Boolean functions for …

A new framework concerning the construction of small-order resilient Boolean functions
whose nonlinearity is strictly greater than 2 n-1-2 [n/2] is given. First, a generalized Maiorana …

In this paper, we give an efficient method for constructing a large set of disjoint spectra
functions without linear structures, which are not equivalent to partially linear functions. This …

In this paper, we present a class of $2 k $-variable balanced Boolean functions and a class
of $2 k $-variable $1 $-resilient Boolean functions for an integer $ k\ge 2$, which both have …

In this paper, we present theoretical constructions of Rotation Symmetric Boolean Functions
(RSBFs) on odd number of variables with the maximum possible algebraic immunity. To get …

This paper considers the construction of resilient Boolean functions on an odd number of
variables with strictly almost optimal (SAO) nonlinearity. Through introducing the …

Nonlinearity is one of the most challenging combinatorial property in the domain of Boolean
function research. Obtaining nonlinearity greater than the bent concatenation bound for odd …

Esta tesis establece los fundamentos teóricos y diseña una colección abierta de clases C++
denominada VBF (Vector Boolean Functions) para analizar funciones booleanas vectoriales …

This paper presents a construction for a class of 1-resilient functions with optimal algebraic
immunity on an even number of variables. The construction is based on the concatenation of …

Abstract Very recently, Kavut and Yucel identified 9-variable Boolean functions having
nonlinearity 242, which is currently the best known. However, any of these functions do not …