Some Results on Generalized Difference Sets

Sequences with ideal correlation functions have important applications in communications such as CDMA, FDMA, etc. It has been shown that difference sets can be used to construct such sequences. The author extends Pott and Bradley’s method to a much broader case by proposing the concept of generalized difference sets. Some necessary conditions for the existence of generalized difference sets are established by means of some Diophantine equations. The author also provides an algorithm to determine the existence of generalized difference sets in the cyclic group . Some examples are presented to illustrate that our method works. The research is partially supported by National Natural Science Foundation of China under Grant No. 10771100.