On abelian $(2^{2m+1}(2^{m-1}+1), 2^m(2^m+1), 2^m)$-difference sets

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75977In this paper we prove that an abelian group contains $(2^{2m+1}(2^{m-1}+1), 2^m(2^m+1), 2^m)$-difference sets with $m\geqslant 3$ if and only if it contains an elementary abelian 2-group of order $2^{2m}$. Our proof shows that the method of constructing such difference sets is essentially unique.18 pagesCombinatoricsNumber Theory05B10On abelian $(2^{2m+1}(2^{m-1}+1), 2^m(2^m+1), 2^m)$-difference setstext