Algebraic and Combinatorial Characterization of Latin squares I
József Dénes (1967)
Matematický časopis
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József Dénes (1967)
Matematický časopis
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Czesław Kościelny (2002)
International Journal of Applied Mathematics and Computer Science
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A method of generating a practically unlimited number of quasigroups of a (theoretically) arbitrary order using the computer algebra system Maple 7 is presented. This problem is crucial to cryptography and its solution permits to implement practical quasigroup-based endomorphic cryptosystems. The order of a quasigroup usually equals the number of characters of the alphabet used for recording both the plaintext and the ciphertext. From the practical viewpoint, the most important quasigroups...
Stones, Douglas S. (2010)
The Electronic Journal of Combinatorics [electronic only]
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Aleksandar Krapež, Dejan Živković (2010)
Publications de l'Institut Mathématique
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Belousov D. Valentin, Stojaković M. Zoran (1976)
Zbornik Radova
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Aleš Drápal (2005)
Czechoslovak Mathematical Journal
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If is a quasigroup that is free in the class of all quasigroups which are isotopic to an Abelian group, then its multiplication group is a Frobenius group. Conversely, if is a Frobenius group, a quasigroup, then has to be isotopic to an Abelian group. If is, in addition, finite, then it must be a central quasigroup (a -quasigroup).
Anthony B. Evans (2014)
Commentationes Mathematicae Universitatis Carolinae
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We consider two classes of latin squares that are prolongations of Cayley tables of finite abelian groups. We will show that all squares in the first of these classes are confirmed bachelor squares, squares that have no orthogonal mate and contain at least one cell though which no transversal passes, while none of the squares in the second class can be included in any set of three mutually orthogonal latin squares.