23 does not divide the order of the group of a (72,36,16) doubly even code (Corresp.)

An interesting open question is whether a doubly even code exists. In [3] the odd prime numbers which can divide the order of the group of were determined and is the largest of these. Twenty-three is eliminated by reducing the problem to the consideration of codes, each of which is shown to have minimum weight or less. One of these codes, denoted by , arises from the construction where and are in one quadratic residue code and is in the other. The weight distribution of is given.