Super-simple Balanced Incomplete Block Designs With Large Index

A design is said to be super-simple if the intersection of any two bolcks has at most two elements.Such designs can be used to construct superimposed codes and designs with maximally different blocks.If a super-simple design is cyclic,it can be used to construct an optical orthogonal code.In this thesis,we devoted to the existence of two super-simple balanced incomplete block designs with large index,that is,prove that the necessary conditions for the existence of a super-simple(v,4,8)-BIBD and a super-simple(v,4,9)-BIBD are sufficient.This thesis consists of six chapters.In chapter 1,we introduce some terminology and notation,summarize the background and the main contents of this thesis.In chapter 2,we introduce the constructions usually used to construct super-simple designs.In chapter 3 and 4,we prove the main results of the thesis.In chapter 5,we give the application of the main conclusions.In chapter 6,we give two luther research problems.