On mutually μ-intersecting quasi-Hermitian varieties with some applications

Let W be a non-empty set of points of a finite Desarguesian projective space PG(n, q). A collection of varieties of PG(n, q) is mutually mu-intersecting (relatively to X97) if its elements meet all W in the same number of points and pairwise intersect in W in exactly mu points. Here, we construct a new family of mutually mu-intersecting algebraic varieties by using certain quasi-Hermitian varieties of PG(n, q(2)), where q is any prime power. With the help of these quasi-Hermitian varieties we provide a new construction of 5-dimensional MDS codes over F-q as well as an infinite family of simple orthogonal arrays OA(q(2n-1), q(2n-2), q, 2) of index mu = q(2n-3).