Encyclopaedia of DesignTheory: A self-orthogonal Latin square

A Latin square cannot, obviously, be self-orthogonal. So the term "self-orthogonal" means "orthogonal to its transpose". That is, a Latin square is self-orthogonal if, for any pair (k,l) of symbols, there is a cell (i,j) which contains the entry k such that the cell (j,i) contains the entry l.

For example, if we superimpose the square with (i,j) entry (2i+j) mod 5 on its transpose, we see that this square is "self-orthogonal".

00	12	24	31	43
21	33	40	02	14
42	04	11	23	30
13	20	32	44	01
34	41	03	10	22

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Peter J. Cameron
29 October 2002