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Latin squares over Abelian groups

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Abstract

In this paper, parametric families of Latin squares over Boolean vectors and prime fields constructed earlier are generalized to the case of Abelian groups. Some criteria for realizability of this construction are presented. Some classification results are also given.

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References

  1. J. Dénes and A. Keedwell, Latin Squares and Their Applications, Budapest (1974).

  2. V. A. Nosov, “On construction of classes of Latin squares in the Boolean database,” Intellekt. Sistemy, 4, No. 3–4, 307–320 (1999).

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  3. V. A. Nosov, “Constructing a parametric family of Latin squares in the vector database,” Intellekt. Sistemy, 8, No. 1–4, 517–528 (2004).

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  4. V. A. Nosov and A. E. Pankratiev, “Latin squares over Abelian groups,” in: Mathematical Methods and Applications. Proc. XIV Math. Readings of MGSU (January 28–31, 2005) [in Russian], Moscow (2005), pp. 72–76.

  5. C. Shannon, “Communication theory of secrecy systems,” Bell System Tech. J., 28, No. 4, 656–715 (1949).

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Authors and Affiliations

  1. Department of Mechanics and Mathematics, Chair of Mathematical Theory of Intelligent Systems, Moscow State University, Russia

    V. A. Nosov & A. E. Pankratiev

Authors
  1. V. A. Nosov
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  2. A. E. Pankratiev
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 3, pp. 65–71, 2006.

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Nosov, V.A., Pankratiev, A.E. Latin squares over Abelian groups. J Math Sci 149, 1230–1234 (2008). https://doi.org/10.1007/s10958-008-0061-9

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  • DOI: https://doi.org/10.1007/s10958-008-0061-9

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