, Volume 70, Issue 4, pp 349–357 | Cite as

On the Existence of Totally Anti-Symmetric Quasigroups of Order 4k+2



Totally anti-symmetric quasigroups are employed in check digit systems. We give counterexamples to a conjecture of Ecker and Poch and show that there are totally anti-symmetric quasigroups for all orders n≡0,1,34, n=4(5k+2)+2, and n=4(7k+3)+2. We prove that finite totally anti-symmetric quasigroups possess a transversal, and we give a useful condition for quasigroups not to have a transversal.


05B15 orthogonal arrays latin squares room squares 20N05 loops quasigroups 94B60 other types of codes 


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Copyright information

© Springer-Verlag Wien 2003

Authors and Affiliations

  1. 1.DautphetalGermany

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