Research On The Constructions Of Zero-Difference Balanced Function And Its Applications

Zero-difference balance function is a generalization of perfect nonlinear function,which was introduced by Cunsheng Ding in 2008.It has a wide applications in coding and cryptography.This paper mainly studies the zero-difference balance function and its applica-tion.We construct two new classes of zero-difference balance function and apply them to construct the optimal constant composition codes and difference systems of sets.Our main results are summarized as follows:1)We define two classes of cyclotomic coset,via using the zero-difference balance function in(Z x Z,+)by Zha et al..We also construct a new class of zero-difference balance function in(Fpm × ZFpn,+),via using cyclotomic coset,.2)Via using the zero-difference balance function derived from fermat quotient by Ye et al.,we construct several new classes of zero-difference balanced function by using polynomial quotient.3)Based on the new proposed zero-difference balanced functions,we also construct the optimal frequency hopping sequence,frequency hopping sequence sets,the optimal constant composition codes and difference systems of sets.