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Graphs and Combinatorics

, Volume 2, Issue 1, pp 309–316 | Cite as

An Erdös-Ko-Rado theorem for regular intersecting families of octads

  • A. E. Brouwer
  • A. R. Calderbank
Article

Abstract

Codewords of weight 8 in the [24, 12] binary Golay code are called octads. A family of octads is said to be a regular intersecting family if is a 1-design and |x ∩ y| ≠ 0 for allx, y ∈ ℱ. We prove that if is a regular intersecting family of octads then || ≤ 69. Equality holds if and only if is a quasi-symmetric 2-(24, 8, 7) design. We then apply techniques from coding theory to prove nonexistence of this extremal configuration.

Keywords

Golay Code Intersecting Family Extremal Configuration Binary Golay Code 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • A. E. Brouwer
    • 1
  • A. R. Calderbank
    • 2
  1. 1.Institut for Elektroniske SystemerAalborg UniversitetcenterAalborgDenmark
  2. 2.Mathematical Sciences Research CenterAT&T Bell LaboratoriesMurray HillUSA

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