The Combinatorial Constructions Of Zero-difference Balanced Functions

Zero-difference balanced(ZDB)functions are combinatorial structures which were defined by Ding in studying constant composition codes(CCCs).Constant composition codes are a special class of constant weight codes which were used to research balanced schedules and electric power communications in communications engineering.They are widely used in multiple access communication,the coding for DNA,frequency-hopping sequences and the modulation for spherical codes etc..Zero-difference balanced functions can also be used in the constructions of difference system of sets(DSSs)which are combinatorial structures defined by Levenstein in constructing comma-free codes.Ding constructed zero-difference balanced functions by trace functions over finite fields in 2008.Zhou et al.developed two generic constructions of zero-difference balanced functions applying functions with difference-balanced property in 2012.Cai et al.presented a new construction of zero-difference balanced functions using a generalized cyclotomy in 2013.Wang et al.exhibited a generic construction of zero-difference balanced functions in 2014.Ding et al.proposed three new classes of zero-difference balanced functions in the same year.Zha et al.got some cyclotomy constructions of zero-difference balanced functions in 2015.Ding et al.pointed out the equivalence between zero-difference balanced functions and partitioned difference families(PDFs).Partitioned difference families were defined by Ding and Yin in researching constant composition codes.Yin and Wang et al.presented some partitioned difference families by cyclotomy theory over finite fields.Wang et al.introduced the methods by applying 1-rotational resolvable balanced incomplete block designs.Zhu also gave some partitioned difference families using splitting and integrating cyclotomies.In the first chapter of this paper,some related conceptions and conclusions are introduced.In the second chapter,we construct some new families of zero-difference balanced functions from partitioned difference families.In the third chapter,we introduce the applications of zero-difference balanced functions in optimal constant composition codes,perfect difference system of sets and frequency-hopping sequences.