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Codes from Generalized Hexagons

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Abstract

In this paper, we construct some codes that arise from generalized hexagons with small parameters. As our main result we discover two new projective two-weight codes constructed from two-character sets in PG(5,4) and PG(11,2). These in turn are constructed using a new distance-2-ovoid of the classical generalized hexagon H(4). Also the corresponding strongly regular graph is new. The two-character set is the union of two orbits in PG(5,4) under the action of L2(13).

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Authors and Affiliations

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

    A. De Wispelaere & H. Van Maldeghem

Authors
  1. A. De Wispelaere
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  2. H. Van Maldeghem
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Corresponding author

Correspondence to A. De Wispelaere.

Additional information

Communicated by: R. Calderbank

The first Author is Research Assistant of the Fund for Scientific Research - Flanders (Belgium) (F.W.O)

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De Wispelaere, A., Van Maldeghem, H. Codes from Generalized Hexagons. Des Codes Crypt 37, 435–448 (2005). https://doi.org/10.1007/s10623-005-4035-3

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  • DOI: https://doi.org/10.1007/s10623-005-4035-3

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