On Almost Difference Sets

For its close relation to cryptography , coding theory and sequences , almost difference sets have attracted many scholars ' attention. Firstly, Davis called a special kind of divisible difference set (DDS) almost difference set. Another kind of almost difference sets was defined by Ding etc. for constructing binary sequence with three-level autocorrelation. Lastly Arasu etc. give a more extensive definition of almost difference sets and establish relations between some difference sets and some almost difference sets. So far the known existincc results are limited.This book is composed of following sections: In the first section, we present the nessary definitions and give a well-rounded treatment of known families of almost difference sets; In the second section, we discuss the possibility of constructing almost difference sets with 2 , 4 and 6 order cyclotomy classes; In the third section, we construct two new families of almost difference sets by using cyclotomy modulo pq, where p and q are distinct primes; In the last section,we discuss the methord to construct almost difference sets with difference sets.