Sets in Zn with distinct sums of pairs

Authors:
Harri Haanpää;Antti Huima;Patric Östergård
Affiliations:
Department of Computer Science and Engineering, Helsinki University of Technology, P.O. Box 5400, FIN-02015-HUT, Finland;Department of Computer Science and Engineering, Helsinki University of Technology, P.O. Box 5400, FIN-02015-HUT, Finland;Department of Electrical and Communications Engineering, Helsinki University of Technology, P.O. Box 3000, FIN-02015-HUT, Finland
Venue:
Discrete Applied Mathematics
Year:
2004

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Abstract

A subset S={s"1,...,s"k} of an abelian group G is called an S"t-set of size k if all sums of t different elements in S are distinct. A function with applications in coding theory, v"@c(k) denotes the order of the smallest cyclic group in which an S"2-set of size k exists. A lower bound for v"@c(k) is given in this study, and exact values of v"@c(k) are obtained for k=