The Combinatorial Constructions Of Near Zero-difference Balanced Functions

In 2008,Ding introduced a class of combinatorial functions called zero-difference balanced functions((5).Zero-difference balanced functions have been widely applied in coding theory and communications.They can be used to construct constant weight codes()? frequency hopping sequences( )? the difference system of sets()and so on.Near zero-difference balanced functions( (5)are considered a natural extension of zero-difference balanced functions,and they were put forword in 2014 by Yin Jianxing and A Kejun.They can also be used to construct construct constant weight codes?frequency hopping sequences?the difference system of sets etc,and more flexible.In this paper,we mainly study the combinatorial constructions of near zero-difference balanced functions.Based on cyclotomic theory in finite field and combined with related conclusions of different sets()? almost different sets()? different families()?almost different families()in the theory of combinatorial designs,we show some recursive constructions and directly constructions of near zero-difference balanced functions.In the article,we introduce some related concepts and the combinatorial characteristic of near zero-difference balanced functions in the first chapter.In the second chapter,we get some infinite classes of partitioned almost difference families( )applying direct and recursive constructions.In the third chapter,we study a class of special near zero-difference balanced functions and their corresponding special partitioned almost difference families.As the equivalence between them,more near zero-difference balanced functions are presented.At the end,we talk about the applications of near zero-difference balanced functions.