Tightening Turyn's bound for Hadamard difference sets

AbuGhneim, Omar A. ; Smith, Ken W.

Journal of Algebraic Combinatorics, Tome 27 (2008) no. 2, pp. 187-203.

Résumé

Summary: This work examines the existence of ($4 q ^{2},2 q ^{2} - q, q ^{2} - q$) difference sets, for $q= p ^{ f }$, where $p$ is a prime and $f$ is a positive integer. Suppose that $G$ is a group of order $4 q ^{2}$ which has a normal subgroup $K$ of order $q$ such that $G/ K \cong C _{ q }\times C _{2}\times C _{2}$, where $C _{ q }, C _{2}$ are the cyclic groups of order $q$ and 2 respectively. Under the assumption that $p$ is greater than or equal to 5, this work shows that $G$ does not admit ($4 q ^{2},2 q ^{2} - q, q ^{2} - q$) difference sets.

Détail

Keywords: keywords Hadamard difference sets, intersection numbers, characters