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stslam2017-02-22 14:03:10
Mathematics
stslam, 2017-02-22 14:03:10

How to construct Latin Damm square for arbitrary order N?

According to the finished square (N==10) - everything is simple, take it and use it.
But not every square is suitable.
For example, if we take the following square (N==10), then for
572 and 527 - the check digit is the same (==0)

{ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }, 
{ 9, 0, 1, 2, 3, 4, 5, 6, 7, 8 }, 
{ 8, 9, 0, 1, 2, 3, 4, 5, 6, 7 }, 
{ 7, 8, 9, 0, 1, 2, 3, 4, 5, 6 }, 
{ 6, 7, 8, 9, 0, 1, 2, 3, 4, 5 }, 
{ 5, 6, 7, 8, 9, 0, 1, 2, 3, 4 }, 
{ 4, 5, 6, 7, 8, 9, 0, 1, 2, 3 }, 
{ 3, 4, 5, 6, 7, 8, 9, 0, 1, 2 }, 
{ 2, 3, 4, 5, 6, 7, 8, 9, 0, 1 }, 
{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 }

By the way, in the given link to the corresponding Wikipedia article - Quasigroups for the Damm algorithm up to order 64 , not all squares are "good" either.
So the question is: What is the algorithm?

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