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Designs, Codes and Cryptography

, Volume 71, Issue 3, pp 541–545 | Cite as

A characterisation of tangent subplanes of PG(2, q 3)

  • S. G. Barwick
  • Wen-Ai Jackson
Article

Abstract

In “Barwick and Jackson (Finite Fields Appl. 18:93–107 2012)”, the authors determine the representation of Order-q-subplanes s and order-q-sublines of PG(2, q 3) in the Bruck–Bose representation in PG(6, q). In particular, they showed that an Order-q-subplanes of PG(2, q 3) corresponds to a certain ruled surface in PG(6, q). In this article we show that the converse holds, namely that any ruled surface satisfying the required properties corresponds to a tangent Order-q-subplanes of PG(2, q 3).

Keywords

Bruck–Bose representation PG(2, q3Order q subplanes 

Mathematics Subject Classification

51E20 

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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.School of MathematicsUniversity of AdelaideAdelaideAustralia

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