Extremal set theory, cubic forms on F₂ⁿ and Hurwitz square identities

Original · EN

We consider a family, F, of subsets of an n-set such that the cardinality of the symmetric difference of any two elements F,F' is not a multiple of 4. We prove that the maximal size of F is bounded by 2n, unless n≡34 when it is bounded by 2n+2. Our method uses cubic forms on F₂ⁿ and the Hurwitz-Radon theory of square identities. We also apply this theory to obtain some information about boolean cubic forms and so-called additive quadruples.