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

In this paper we prove that an abelian group contains $(2^{2m+1}(2^{m-1}+1), 2^m(2^m+1), 2^m) $- d i f f e r e n c e s e t s w i t h$ m\geqslant 3$ if and only if it contains an elementary abelian 2-group of order $2^{2 m}$ . Our proof shows that the method of constructing such difference sets is essentially unique.

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

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

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On abelian (22m+1(2m−1+1),2m(2m+1),2m)(22m+1(2m−1+1),2m(2m+1),2m)-difference sets

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On abelian (22m+1(2m−1+1),2m(2m+1),2m)(22m+1(2m−1+1),2m(2m+1),2m)-difference sets

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

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

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