On varieties defined by large sets of quadrics and their application to error-correcting codes
Let U be a [Formula presented]-dimensional subspace of quadratic forms defined on Fk with the property that U does not contain any reducible quadratic form. Let V(U) be the points of PG(k−1,F) which are zeros of all quadratic forms in U. We will prove that if there is a group G which fixes U and no line of PG(k−1,F) and V(U) spans PG(k−1,F) then any hyperplane of PG(k−1,F) is incident with at most k points of V(U).