Codes in the q-ary Lee Hypercube

Let F q = {0, 1, . . . , q -1} be an alphabet of size q, so that F n q is the q-ary hypercube of dimension n. Let x = (x 1 , . . . , x n ) and y = (y 1 , . . . , y n ) be two elements in F n q . The Lee distance between x and y is equal to