Some new non-cyclic Latin squares that have cyclic and Youden properties

This note gives what is believed to be the first published example of a symmetric 11 x 11 Latin square which, although not cyclic, has the property that the permutation between any two rows is an 11-cycle. The square has the further property that two subsets of its rows constitute 5 x 11 Youden squares. The note shows how this 11 x 11 Latin square can be obtained by a general construction for n x n Latin squares where n is prime with n greater than or equal to 11. The permutation between any two rows of any Latin square obtained by the general construction is an n-cycle; two subsets of (n - 1)/2 rows from the Latin square constitute Youden squares if n = 3 (mod 8).