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Classification of Quasigroups by Random Walk on Torus
Smile Markovski,Danilo Gligoroski,Jasen Markovski 한국전산응용수학회 2005 Journal of applied mathematics & informatics Vol.19 No.1-2
Quasigroups are algebraic structures closely related to Latin squares which have many different applications. There are several classificationsof quasigroups based on their algebraic properties. In this paperwe 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. Weperformed tests for randomnessof the obtained pseudo-random sequencesby randomwalks on torus. The randomness tests provided an empirical classification of quasi-groups.
CLASSIFICATION OF QUASIGROUPS BY RANDOM WALK ON TORUS
MARKOVSKI, SMILE,GLIGOROSKI, DANILO,MARKOVSKI, JASEN 한국전산응용수학회 2005 Journal of applied mathematics & informatics Vol.19 No.1
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 quasigroups.