A sharp exponent bound for McFarland difference sets with p=2

[摘要] We show that under the self-conjugacy condition a McFarland difference set with p = 2 and f greater than or equal to 2 in an abelian group G can only exist, if the exponent of the Sylow 2-subgroup does not exceed 4. The method also works for odd p (where the exponent bound is p and is necessary and sufficient), so that we obtain a unified proof of the exponent bounds for McFarland difference sets. We also correct a mistake in the proof of an exponent bound for (320, 88, 24)-difference sets in a previous paper. (C) 1997 Academic Press.

[发布日期] 1997-11-01