On the Automorphism Group of a Binary Self-Dual Doubly Even $[{72, 36, 16}]$ Code

We prove that the automorphism group of a binary self-dual doubly even [72, 36, 16] code has order 5, 7, 10, 14 or <i>d</i> where <i>d</i> divides 18 or 24, or it is <i>A</i><sub>4</sub> × <i>C</i><sub>3</sub>.

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