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

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 . 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.