An Erdos-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 F of octads is said to be a regular intersecting family if F is a 1-design and |x inter y| not= 0 for all x,y epsilon F. We prove that if F is a regular intersecting family of octads then |F| = 69. Equality holds if and only if F is a quasi-symmetric 2-(24,8,7) design. We then apply techniques from coding theory to prove nonexistence of this extremal configuration.