The automorphism group of the doubly-even [72,36,16] code can only be of order 1, 3 or 5

Steven T Dougherty, Suat Karadeniz, Bahattin Yildiz

We prove that a putative $[72,36,16]$ code is not the image of linear code over $\ZZ_4$, $\FF_2 + u \FF_2$ or $\FF_2+v\FF_2$, thus proving that the extremal doubly even $[72,36,16]…