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Note on the existence of translation nets

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Abstract

We exhibit a class of (2k + 1, 22k)-translation nets with nonabelian translation group, for any natural k. At the same time, it is the first infinite class of translation nets known to admit nonisomorphic translation groups for each of its elements.

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References

  1. Hachenberger D. (1991). Constructions of large translation nets with nonabelian translation groups. Des. Codes Cryptogr. 1, 219–236

    Article  MATH  MathSciNet  Google Scholar 

  2. Payne S.E., Thas J.A.: Finite Generalized Quadrangles. Research Notes in Mathematics, vol. 110. Pitman Advanced Publishing Program, Boston (1984).

  3. Rostermundt R.R.: Elation groups of the Hermitian surface H(3, q 2) over a finite field of characteristic 2. Innov. Incidence Geom. (to appear).

  4. Sprague A.P. (1982). Translation nets. Mitt. Math. Sem. Giessen 157, 46–68

    MathSciNet  Google Scholar 

  5. Thas K. (2006). Some basic conjectures on elation generalized quadrangles, and their solutions. Bull. Belgian Math. Soc.—Simon Stevin 12, 909–918

    MathSciNet  Google Scholar 

  6. Thas J.A., Thas K., Van Maldeghem H. (2006). Translation Generalized Quadrangles. Series in Pure Mathematics vol. 26. World Scientific, Singapore

    Google Scholar 

  7. Thas K.: Lectures on Elation Quadrangles. Monograph, Appr. 100 pp. (submitted).

  8. Thas K.: Central aspects of skew translation generalized quadrangles, Appr. 150 pp. (in preparation).

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Authors and Affiliations

  1. Department of Pure Mathematics and Computer Algebra, Ghent University, Krijgslaan 281, S22, 9000, Ghent, Belgium

    Koen Thas

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  1. Koen Thas
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Correspondence to Koen Thas.

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Communicated by M.J. de Resmini.

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Thas, K. Note on the existence of translation nets. Des. Codes Cryptogr. 48, 105–107 (2008). https://doi.org/10.1007/s10623-008-9201-y

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  • DOI: https://doi.org/10.1007/s10623-008-9201-y

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