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

Mutually intersecting varieties of a finite Desarguesian projective space are varieties with the same size, such that the intersection of two of them contains the same number of points. Here, we show the existence of a new family of mutually intersecting varieties by using certain quasi-Hermitian varieties of PG(n,q²), 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 Fq as well as an infinite family of simple orthogonal arrays OA(q²ⁿ⁻¹,q²ⁿ⁻²,q,2) of index μ=q²ⁿ⁻³.