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Integral automorphisms of affine spaces over finite fields

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Abstract

A permutation of the point set of the affine space \({{\mathrm{AG}}}(n,q)\) is called an integral automorphism if it preserves the integral distance defined among the points. In this paper, we complete the classification of the integral automorphisms of \({{\mathrm{AG}}}(n,q)\) for \(n\ge 3\).

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References

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Acknowledgments

The authors are grateful to Marko Orel for drawing their attention to the work of Lester [11]. This research was supported in part by the OTKA-ARRS Slovenian-Hungarian Joint Research Project, Grant No. NN 114614 (in Hungary) and N1-0032 (in Slovenia). The first two authors also thank the Slovenian Research Agency ARRS (Research Program P1-0285 and Research Projects N1-0038, J1-5433, J1-6720 and J1-6743), and the second author was also supported in part by WoodWisdom-Net+, \(\hbox {W}^3\hbox {B}\).

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Authors and Affiliations

  1. IAM and FAMNIT, University of Primorska, Glagoljaška 8, 6000, Koper, Slovenia

    István Kovács & Klavdija Kutnar

  2. Institute of Mathematics and Informatics, University of Pécs, Ifjúság útja 6, Pécs, 7624, Hungary

    János Ruff

  3. Institute of Mathematics, Eötvös University & MTA-ELTE Geometric and Algebraic Combinatorics Research Group, Pázmány P. s. 1/C, Budapest, 1117, Hungary

    Tamás Szőnyi

Authors
  1. István Kovács
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  2. Klavdija Kutnar
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  3. János Ruff
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  4. Tamás Szőnyi
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Corresponding author

Correspondence to István Kovács.

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This is one of several papers published in Designs, Codes and Cryptography comprising the special issue in honor of Andries Brouwer’s 65th birthday.

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Kovács, I., Kutnar, K., Ruff, J. et al. Integral automorphisms of affine spaces over finite fields. Des. Codes Cryptogr. 84, 181–188 (2017). https://doi.org/10.1007/s10623-016-0246-z

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  • DOI: https://doi.org/10.1007/s10623-016-0246-z

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