Magic Squares and Sudoku

We introduce a family of magic squares, called linear magic squares, and show that any parallel linear sudoku solution of sufficiently large order can be relabeled so that all of its subsquares are linear magic. As a consequence, we show that if n has prime factorization p1 1 · · · p kt t and q = min{p k j j | 1 ≤ j ≤ t}, then there is a family of q(q − 1) mutually orthogonal magic sudoku solutions of order n2 whenever q > 3; such an orthogonal family is complete if n is a prime power.