
Encyclopaedia of DesignTheory: A selforthogonal Latin square 
A Latin square cannot, obviously, be selforthogonal. So the term "selforthogonal" means "orthogonal to its transpose". That is, a Latin square is selforthogonal 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 "selforthogonal".
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Peter J. Cameron
29 October 2002