Judging of the orthogonal system over rings Z_N

In the research of block cipher,orthogonal system is widely regarded.Permutation isa kind of special orthogonal systems,and it has important applications in cryptology as iswell known.The orthogonal system over finite field has been made in a large number ofresearches.In the research of orthogonal system,an important problem is how toefficiently judge whether a group of functions can form an orthogonal system,and the