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The Largest Cap in AG(4, 4) and Its Uniqueness

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Abstract

We show that 40 is the maximum number of points of a cap in AG(4, 4). Up to semi-linear transformations there is only one such 40-cap. Its group of automorphisms is a semidirect product of an elementary abelian group of order 16 and the alternating group A 5.

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References

  1. A. E. Brouwer, Data base of bounds for the minimum distance for linear codes, URL http://www.win.tue.nl/~aeb/voorlincod.html

  2. Y. Edel and J. Bierbrauer, 41 is the largest size of a cap in PG(4, 4), Designs, Codes and Cryptography, Vol. 16 (1999) pp. 151–160.

    Google Scholar 

  3. Y. Edel, S. Ferret, I. Landjev and L. Storme, The classification of the largest caps in AG(5, 3), Journal of Combinatorial Theory A, Vol. 99 (2002) pp. 95–110.

    Google Scholar 

  4. J. H. Griesmer, A bound for error correcting codes, IBM Journal Research Development, Vol. 4 (1960) pp. 532–542.

    Google Scholar 

  5. B. Groneick and S. Grosse, New binary codes, IEEE Transactions on Information Theory, Vol. 40 (1994) pp. 510–512.

    Google Scholar 

  6. R. Hill, The largest size of cap in S 5,3, Rend. Acc. Naz. Lincei, Vol. 54, No. 8 (1973) pp. 378–384.

    Google Scholar 

  7. G. Pellegrino, Sul massimo ordine delle calotte in S 4,3, Matematiche (Catania), Vol. 25 (1970) pp. 1–9.

    Google Scholar 

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Authors and Affiliations

  1. Mathematisches Institut der Universität, Im Neuenheimer Feld 288, 69120, Heidelberg, Germany

    Yves Edel

  2. Department of Mathematical Sciences, Michigan Technological University, Houghton, Michigan, 49931, USA

    Jürgen Bierbrauer

Authors
  1. Yves Edel
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  2. Jürgen Bierbrauer
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Edel, Y., Bierbrauer, J. The Largest Cap in AG(4, 4) and Its Uniqueness. Designs, Codes and Cryptography 29, 99–104 (2003). https://doi.org/10.1023/A:1024144223076

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  • DOI: https://doi.org/10.1023/A:1024144223076

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