Extremal self-dual lattices exist only in dimensions 1 to 8

@inproceedings{Conway1978ExtremalSL,
  title={Extremal self-dual lattices exist only in dimensions 1 to 8},
  author={John H. Conway and Andrew M. Odlyzko and N. J. A. Sloane},
  year={1978}
}
It is known that if A is a self-dual lattice in R", then min {u-u | u e A, u # 0} < (M/8) + 1. If equality holds the lattice is called extremal. In this paper we find all the extremal lattices: there are unique lattices in dimensions 1, 2, 3, 4, 5, 6, 7, 8, 12, 14, 15, 23, 24 and no others. 
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