Properties Of Multioutput M-valued Logical Functions

Using concepts of probability, algebra and spectral theory, we study properties of correlation degree and correlation coefficient of multioutput m-valued logical functions. Also, we study properties of multioutput generalized bent functions.The main results are as follows:First, we present definition of correlation degree of multioutput m-valued logical functions. We discuss its basic properties and show relationship between correlation degree and independency. Then we define correlation coefficient of multioutput m-valued logical functions and give proof of its properties. Finally we show relationship between correlation coefficient and independency.Another part of our work begins with definition of multioutput generalized bent functions. We show their spectral characteristics and give equivalence definition using generalized first order Chrestenson cyclic spectrum. Also we calculate rate of accordance between multioutput generalized bent functions and multioutput m-valued affine functions. Then we define multioutput m-valued perfect nonlinear functions and show relationship between them and multioutput generalized bent functions. Finally we give two ways of constructions of multioutput generalized bent functions.