Strongly symmetric self-orthogonal diagonal Latin squares and Yang Hui type magic squares

In this paper, a strongly symmetric self-orthogonal diagonal Latin square of order n with a special property (∗SSSODLS(n)) is introduced. It is proved that a ∗SSSODLS(n) exists if and only if n≡0(mod4) and n≠4. As an application, it is shown that there exists a Yang Hui type magic square YMS(n,4) if and only if n≡0(mod4) and n≠4.