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

March 2013

DOI:10.48550/arXiv.1303.4920

Authors:

Steven T. Dougherty

University of Scranton

Texas A&M University – Texarkana

Bahattin Yildiz

Northern Arizona University

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]-binary code cannot have an automorphism group containing a fixed point-free involution. Combining this with the previously proved result by Bouyuklieva that such a code cannot have an automorphism group containing an involution with fixed points, we conclude that the automorphism group of the [72,36,16]-code cannot be of even order, leaving 3 and 5 as the only possibilities.

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