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Enumeration of orthogonal Buekenhout unitals

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Abstract

In this paper we develop general techniques for enumerating orthogonal Buekenhout unitals embedded in two-dimensional translation planes. We then apply these techniques in the regular nearfield planes, the odd-order Hall planes, and the odd-order flag-transitive affine planes. Stabilizers of the resulting unitals also are computed.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, West Virginia State University, Institute, WV, 25112, USA

    R. D. Baker

  2. Department of Mathematical Science, University of Delaware, Newark, DE, 19716, USA

    G. L. Ebert

  3. Regent University, Virginia Beach, VA, 23464, USA

    K. L. Wantz

Authors
  1. R. D. Baker
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  2. G. L. Ebert
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  3. K. L. Wantz
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Corresponding author

Correspondence to G. L. Ebert.

Additional information

Communicated by Ron Mullin/Rainer Steinwandt.

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Baker, R.D., Ebert, G.L. & Wantz, K.L. Enumeration of orthogonal Buekenhout unitals. Des. Codes Cryptogr. 55, 261–283 (2010). https://doi.org/10.1007/s10623-009-9330-y

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  • DOI: https://doi.org/10.1007/s10623-009-9330-y

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