Orthogonal Frames in the Leech Lattice and a Type II Code over Z22

In this paper, we consider the problem of the existence of a basis of orthogonal vectors of norm 2k in the Leech lattice. Recently it has been shown that there is such a basis for every k (⩾2) which is not of the form 11r. In this paper, this problem is completely settled by finding such a basis for k=11. This is established by constructing an extremal Type II Z22-code of length 24.