Constructions For Difference Set Pairs

The address code in the new Spread-Spectrum Communication, designed on the theory of dfference set pairs, provides a wider selection of code address to the Spread-Spectrum Communication System. Hence, it is of great theoretical and practical importance to make an in-depth study on difference set pairs.This paper describes the concept of difference set pairs at the very beginning. And then by probing into difference set pairs, a property and five new constructions of difference set pairs is derived. This paper has four chapters. In Chapter 1, the relative definitions and overview are given. In Chapter 2, the relative concepts and properties are given, and one new property is introduced, one can use this property to construct even more difference set pairs from known one. In Chapter 3, two kinds of difference set pairs are obtained with direct constructive method, and the existence of (4t,2t-2,2t,t-1,t-1)—difference set pairs and (2k2+2k+1,2k+1,2k+1,1,2)—difference set pairs is proved. In Chapter 4 the existence of (m2e,me,me,e,e)—difference set pairs and (m2t,mtp,mtp,tp2,tp2)—difference set pairs are proved with Hall polynomials. In Chapter 5,—difference set pairs is constructed based on the ring decomposition.