Existence of Z-cyclic 3PDTWh(p) for Prime p ≡ 1 (mod 4)

Authors:
Xiande Zhang;Gennian Ge
Affiliations:
Department of Mathematics, Zhejiang University, Hangzhou, P.R. China 310027;Department of Mathematics, Zhejiang University, Hangzhou, P.R. China 310027
Venue:
Designs, Codes and Cryptography
Year:
2007

Citing 16
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Abstract

A directed triplewhist tournament on p players overZp is said to have the three-person property ifno two games in the tournament have three common players. Webriefly denote such a design as a 3PDTWh(p). In this paper, weinvestigate the existence of a Z-cyclic 3PDTWh(p) for any primep ≡ 1 (mod 4) and show that such a design existswhenever p ≡ 5, 9, 13 (mod 16) and p ≡29. This result is obtained by applying Weil's theorem. Inaddition, we also prove that a Z-cyclic 3PDTWh(p) existswhenever p ≡ 1 (mod 16) and p p = 257, 769.