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


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.


Golay Code Intersecting Family Extremal Configuration Binary Golay Code 
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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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