English

The automorphism group of a self-dual binary [72,36,16] code does not contain Z7, Z3xZ3, or D10

Information Theory 2012-03-14 v2 math.IT
Authors: Thomas Feulner , Gabriele Nebe
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Abstract

A computer calculation with Magma shows that there is no extremal self-dual binary code C of length 72 that has an automorphism group containing D10, Z3xZ3, or Z7. Combining this with the known results in the literature one obtains that Aut(C) is either Z5 or has order dividing 24.

Keywords

self-dual binary code extremal code automorphism group Magma code length 72 group order

Cite

@article{arxiv.1110.6012,
  title  = {The automorphism group of a self-dual binary [72,36,16] code does not contain Z7, Z3xZ3, or D10},
  author = {Thomas Feulner and Gabriele Nebe},
  journal= {arXiv preprint arXiv:1110.6012},
  year   = {2012}
}

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