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Classification of (0,2)-geometries embedded in AG (3,q)

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Abstract

In De Clerck and Delanote (Des. Codes Cryptogr, 32: 103–110, 2004) it is shown that if a (0,α)-geometry with α ≥  3 is fully embedded in AG (n,q) then it is a linear representation. In De Feyter (J. Combin Theory Ser A, 109(1): 1–23, 2005; Discrete math, 292: 45–54, 2005) the (0,2)-geometries fully embedded in AG(3,q) are classified apart from two open cases. In this paper, we solve these two open cases. This classification for AG(3,q) is used in De Feyter (Adv Geom, 5: 279–292, 2005) to classify the (0,2)-geometries fully embedded in AG(n,q).

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Authors and Affiliations

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

    Nikias De Feyter

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  1. Nikias De Feyter
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Correspondence to Nikias De Feyter.

Additional information

Communicated by J. W. P. Hirschfeld.

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De Feyter, N. Classification of (0,2)-geometries embedded in AG (3,q). Des Codes Crypt 43, 21–32 (2007). https://doi.org/10.1007/s10623-007-9050-0

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  • DOI: https://doi.org/10.1007/s10623-007-9050-0

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