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Designs, Codes and Cryptography

, Volume 9, Issue 1, pp 51–59 | Cite as

Oval Designs in Desarguesian Projective Planes

  • Laurel L. Carpenter
Article

Abstract

Given any projective plane Π of even order qcontaining a hyperoval \({\mathcal{O}}\), a Steiner 2-\(2 - (\left( {_2^q } \right),\tfrac{q}{2},1)\) design can be constructed. The 2-rank of this design is boundedabove by rank2(Π}-q-1. Using a result ofBlokhuis and Moorhouse bm94, we show that this bound is met whenΠ is desarguesian and \({\mathcal{O}}\) is regular.We also show that the block graph of the Steiner 2-design inthis case produces a Hadamard design which is such that the binarycode of the associated 3-design contains a copy of the first-orderReed-Muller code of length 2 2m , whereq=2m.

hyperoval Hadamard oval design Reed-Muller 

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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Laurel L. Carpenter
    • 1
  1. 1.Clemson UniversityClemsonSC

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