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Finite Projective Planes and the Delsarte LP-Bound

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Abstract

We apply an improvement of the Delsarte LP-bound to give a new proof of the non-existence of finite projective planes of order 6, and uniqueness of finite projective planes of order 7. The proof is computer aided, and it is also feasible to apply to higher orders like 8, 9 and, with further improvements, possibly 10 and 12.

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Authors and Affiliations

  1. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Realtanoda u 13-15, H-1053, Budapest, Hungary

    M. Matolcsi

  2. Budapest University of Technology and Economics (BME), Egry J. u. 1, H-1111, Budapest, Hungary

    M. Matolcsi & M. Weiner

Authors
  1. M. Matolcsi
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  2. M. Weiner
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Corresponding author

Correspondence to M. Matolcsi.

Additional information

M. Matolcsi was supported by the ERC-AdG 321104 and by NKFIH Grant No. K109789.

M. Weiner was supported by the ERC-AdG 669240, and by NKFIH Grant No. K124152.

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Matolcsi, M., Weiner, M. Finite Projective Planes and the Delsarte LP-Bound. Anal Math 44, 89–98 (2018). https://doi.org/10.1007/s10476-018-0108-1

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  • DOI: https://doi.org/10.1007/s10476-018-0108-1

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