Geodesic
On Subsets with Intersections of Even Cardinality
Canadian mathematical bulletin, Tome 12 (1969) no. 4, pp. 471-474

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DOI

This paper solves a question posed by P. Erdös:If A1, A2, ..., A are distinct subsets of n elements and if |Ai ∩ Ai| ≡ 0 mod 2 (i ≠ j), then and for each n, there exists a collection of subsets which achieves this bound with equality. 
Berlekamp, E.R. On Subsets with Intersections of Even Cardinality. Canadian mathematical bulletin, Tome 12 (1969) no. 4, pp. 471-474. doi: 10.4153/CMB-1969-059-3
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     title = {On {Subsets} with {Intersections} of {Even} {Cardinality}},
     journal = {Canadian mathematical bulletin},
     pages = {471--474},
     year = {1969},
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     number = {4},
     doi = {10.4153/CMB-1969-059-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-059-3/}
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