Classification of quasigroups by random walk on torus

  • Smile Markovski
  • Danilo Gligoroski
  • Jasen Markovski


Quasigroups are algebraic structures closely related to Latin squares which have many different applications. There are several classifications of quasigroups based on their algebraic properties. In this paper we propose another classification based on the properties of strings obtained by specific quasigroup transformations. More precisely, in our research we identified some quasigroup transformations which can be applied to arbitrary strings to produce pseudo random sequences. We performed tests for randomness of the obtained pseudo-random sequences by random walks on torus. The randomness tests provided an empirical classification of quasi-groups.

AMS Mathematics Subject Classification

20N05 11K45 62P99 

Key words and phrases

Random walk quasigroup transformation χ2 


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Copyright information

© Korean Society for Computational and Applied Mathematics 2005

Authors and Affiliations

  • Smile Markovski
    • 1
  • Danilo Gligoroski
    • 1
  • Jasen Markovski
    • 1
  1. 1.Institute of InformaticsFaculty of SciencesSkopjeMacedonia

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