Intersection-sets in \(PG(n,2)\)
A subset \(X\) of \(PG(n,2)\) is called independent if it is line-free, and a set \(C\) is said to be an \(r\)-intersection-set of \(PG(n,2)\) if \(| C\cap K|\geq r\), for all hyperplanes \(K\). In the paper under review line-free intersection-sets of \(PG(n,2)\) are examined, and their incidence equations are described. The authors construct a line-free subset \(X_n\) of \(PG(n,2)\), for every \(n\geq 3\), which meets every hyperplane in at least \(2^{n-3}\) points. For \(n=3,4,5\), the set \(X_n\) is the unique (up to isomorphism) set having these two properties. Further results on \(r\)-intersection-sets in \(PG(n,2)\), \(n=5,6\) are also given.
scientific article; zbMATH DE number 1057360