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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 code C exists. In [3] the odd prime numbers which can divide the order of the group of C were determined and 23 is the largest of these. Twenty-three is eliminated by reducing the problem to the consideration of 348 codes, each of which is shown to have minimum weight 12 or less. One of these codes, denoted by C' , arises from the (a + x, b + x, a + b + x) construction where a and b are in one quadratic residue code and x is in the other. The weight distribution of C' is given.

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