On construction of non-normal Boolean functions

Abstract Given two non-weakly k-normal Boolean functions on n variables a method is proposed to construct a non-weakly (k + 1)-normal Boolean function on (n + 2)- variables. 1 Introduction A function from Fn2 into F2 is called a Boolean function on n variables. The set of all such functions is denoted by Bn. Boolean functions find extensive applications in designing stream ciphers and block ciphers. High nonlinearity and balancedness are possibly the most important properties that a Boolean function which is being used in cipher systems must possess. In case n is odd finding functions with maximum nonlinearity for n> 7 is an open question. For n even the maximum nonlinearity attainable is 2n-1-