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

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An interesting open question is whether a(72, 36, 16)doubly even codeCexists. In [3] the odd prime numbers which can divide the order of the group ofCwere determined and23is the largest of these. Twenty-three is eliminated by reducing the problem to the consideration of348codes, each of which is shown to have minimum weight12or less. One of these codes, denoted byC', arises from the(a + x, b + x, a + b + x)construction whereaandbare in one quadratic residue code andxis in the other. The weight distribution ofC'is given.

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Information Theory, IEEE Transactions on  (Volume:28 ,  Issue: 1 )