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Journal of Geometry

, Volume 105, Issue 1, pp 33–41 | Cite as

Codes from Hall planes of even order

  • J. D. KeyEmail author
  • T. P. McDonough
  • V. C. Mavron
Article

Abstract

We show that the binary code C of the projective Hall plane \({\mathcal{H}_{q^2}}\) of even order q 2 where q = 2 t , for \({t \geq 2}\) has words of weight 2q 2 in its hull that are not the difference of the incidence vectors of two lines of \({\mathcal{H}_{q^2}}\) ; together with an earlier result for the dual Hall planes of even order, this shows that for all \({t \geq 2}\) the Hall plane and its dual are not tame. We also deduce that \({{\rm dim}(C) > 3^{2t} + 1}\), the dimension of the binary code of the desarguesian projective plane of order 22t , thus supporting the Hamada–Sachar conjecture for this infinite class of planes.

Mathematics Subject Classifications (2010)

94B05 51A35 05B05 

Keywords

Non-desarguesian planes Hamada–Sachar conjecture codes 

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Institute of Mathematical and Physical SciencesAberystwyth UniversityAberystwythUK

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