Abstract
Codewords of weight 8 in the [24, 12] binary Golay code are called octads. A familyℱ of octads is said to be a regular intersecting family ifℱ is a 1-design and |x ∩ y| ≠ 0 for allx, y ∈ ℱ. We prove that ifℱ is a regular intersecting family of octads then |ℱ| ≤ 69. Equality holds if and only ifℱ is a quasi-symmetric 2-(24, 8, 7) design. We then apply techniques from coding theory to prove nonexistence of this extremal configuration.
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Brouwer, A.E., Calderbank, A.R. An Erdös-Ko-Rado theorem for regular intersecting families of octads. Graphs and Combinatorics 2, 309–316 (1986). https://doi.org/10.1007/BF01788105
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DOI: https://doi.org/10.1007/BF01788105