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The study of cyclotomic class and difference set pairs

Sun Cai-feng

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Abstract

In this paper,it study the constructions of the difference set pairs and some necessary conditions for the existence of them in three parts.Firstly,it state the basic definitions and some properties of the difference set pairs and cyclotomic class;Then it construct same families of difference set pairs by means of single cycloomic class,and meantime,take some examples to surrport the clam;Finally,it discuss a guess,the difference set pairs cannot existence in two different cyclotomic classes,through some specific examples camg to the conclusion that the guess is reasonable.And also to explor the research about two different cyclotamic classes's adds construct difference set pairs.

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What this paper is about

In this paper,it study the constructions of the difference set pairs and some necessary conditions for the existence of them in three parts.Firstly,it state the basic definitions and some properties of the difference set pairs and cyclotomic class;Then it construct same families of difference set pairs by means of single cycloomic class,and meantime,take some examples to surrport the clam;Finally,it discuss a guess,the difference set pairs cannot existence in two different cyclotomic classes,through some specific examples camg to the conclusion that the guess is reasonable.And also to explor the research about two different cyclotamic classes's adds construct difference set pairs.

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Available abstract

In this paper,it study the constructions of the difference set pairs and some necessary conditions for the existence of them in three parts.Firstly,it state the basic definitions and some properties of the difference set pairs and cyclotomic class;Then it construct same families of difference set pairs by means of single cycloomic class,and meantime,take some examples to surrport the clam;Finally,it discuss a guess,the difference set pairs cannot existence in two different cyclotomic classes,through some specific examples camg to the conclusion that the guess is reasonable.And also to explor the research about two different cyclotamic classes's adds construct difference set pairs.

Key concepts: Class (philosophy), Set (abstract data type), Construct (python library), Difference set, Mathematics, Significant difference, State (computer science), Discrete mathematics

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