Generalized Difference Sets and Almost Perfect Sequences
广义差集与几乎完美序列

The concept and some preliminary properties of generalized difference sets are proposed. In view of application, generalized difference sets are such a kind of combinatorial structures whose $\pm 1$ characteristic sequences have (at most)triple-valued autocorrelation functions. Therefore, generalized difference sets are not only a generalization in the respect of conception, but also have some application backgrounds. In fact, some examples are given, which show that there are some generalized difference sets such that they are neither divisible difference sets, nor relative difference sets. Moreover, some examples are presented here to illustrate that our methods works for obtaining almost perfect sequences.