Difference sets with few character values |
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Authors: | Tao Feng Sihuang Hu Shuxing Li Gennian Ge |
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Institution: | 1. Department of Mathematics, Zhejiang University, Hangzhou, 310027, Zhejiang, China 2. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China
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Abstract: | The known families of difference sets can be subdivided into three classes: difference sets with Singer parameters, cyclotomic difference sets, and difference sets with gcd \((v,n)>1\) . It is remarkable that all the known difference sets with gcd \((v,n)>1\) have the so-called character divisibility property. Jungnickel and Schmidt (Difference sets: an update. London Math. Soc. Lecture Note Ser., vol. 245, pp. 89–112, Cambridge University Press, Cambridge 1997) posed the problem of constructing difference sets with gcd \((v,n)>1\) that do not satisfy this property. In an attempt to attack this problem, we use difference sets with three nontrivial character values as candidates, and get some necessary conditions. |
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