Bounds And Constructions Of Quasi-Hash Families

The actual backgrounds and definition of quasi-hash families are first put forward in this paper. Quasi-hash families are extended from the separating hash families. There are both having distinctions and connections of quasi-hash families, separating hash families and perfect hash families.This paper consists of the following four parts:In the first chapter, a brief survey of the separating hash families and perfect hash families is given firstly, and also the actual backgrounds and definition of quasi-hash fami-lies; Secondly, the interrelate of quasi-hash families and separating hash families is pointed out, and there are also have closely connections between quasi-hash families and perfect hash families. In the second chapter, the necessary conditions of quasi-hash families are studied. First of all, the graph description of the quasi-hash families is given similarly to the separating hash families, the connection between the quasi-hash families and the linear code is discussed and some basic conclusion is obtained. Secondly, the necessary condi-tions of different parameter quasi-hash families are given in this paper with the method of probability. In the third chapter, the distinctions and connections of the quasi-hash families, separating hash families and the combination design are discussed. In the forth chapter, some constructions of different parameters quasi-hash families are given.