Research Of Almost Difference Set Pairs On Cyclotomic

In order to contribute more high-quality spread spectrum sequences to spread spectrum communication system and expand the research space of spread spectrum sequences.Using almost difference set pairs as a tool to find sequence pairs,better research results of sequence pairs can be obtained indirectly.In this paper,the construction method of almost difference set pairs is studied.Combined with the search performance of computer,several new almost difference set pairs are obtained by classical cyclotomy method.Firstly,according to the definition and properties of the classical cyclotomic class and the definition and properties of almost difference set pairs,this paper designs a search algorithm to construct almost difference set pairs through the classical cyclotomic class.Through this algorithm,a large number of instance data of almost difference set pairs are obtained.Secondly,when screening and summarizing a large number of examples of almost difference set pairs,three theorems of constructing almost difference set pairs by 3-order classical cyclotomic class and three theorems of constructing almost difference set pairs by 5-order classical cyclotomic class are summarized.The theorems are proved by mathematical theory,and the almost difference set pairs are new almost difference set pairs.At the end of each theorem,an example of almost difference set pair of this theorem is given.Finally,four theorems of constructing almost difference set pairs by 8 order classical cyclotomic class and four theorems of constructing almost difference set pairs by 10 order classical cyclotomic class are summarized in the search examples of almost difference set pairs constructed by 8 order and 10 order classical cyclotomic class.All the theorems are new almost difference set pairs.These theorems have also been proved by mathematical theory.The corresponding examples are given after each theorem.According to the property of equivalence relation between almost difference set pairs and sequence pairs,some new kinds of almost difference set pairs constructed in this paper can correspond to ternary autocorrelation binary sequence pairs.