The Constructions Of Difference Set Pairs And Frequency-Hopping Sequences Based On The Cyclotomy

This thesis deals with the generalized cyclotomy and its corresponding appli-cations. The contents are as follows:1. A survey of the generalized cyclotomy and its corresponding properties. We introduce a new generalization of Whiteman generalized cyclotomy.2. We give several new classes of difference set pairs based on cyclotomic class.3. We present a construction of Frequency-hopping sequences set based upon the generalized cyclotomy, and show it is optimal with respect to the average Ham-ming correlation bound.