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- W2950184777 abstract "We prove that an automorphism of order 3 of a putative binary self-dual $$[120, 60, 24]$$ code $$C$$ has no fixed points. Moreover, the order of the automorphism group of $$C$$ divides $$2^acdot 3 cdot 5cdot 7cdot 19cdot 23cdot 29$$ with $$ain mathbb N _0$$ . Automorphisms of odd composite order $$r$$ may occur only for $$r=15, 57$$ or $$r=115$$ with corresponding cycle structures $$3 cdot 5$$ - $$(0,0,8;0), 3cdot 19$$ - $$(2,0,2;0)$$ or $$5 cdot 23$$ - $$(1,0,1;0)$$ respectively. In case that all involutions act fixed point freely we have $$|mathrm{Aut}(C)| le 920$$ , and $$mathrm{Aut}(C)$$ is solvable if it contains an element of prime order $$p ge 7$$ . Moreover, the alternating group $$mathrm{A}_5$$ is the only non-abelian composition factor which may occur in $$mathrm{Aut}(C)$$ ." @default.
- W2950184777 created "2019-06-27" @default.
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- W2950184777 date "2013-06-26" @default.
- W2950184777 modified "2023-09-25" @default.
- W2950184777 title "On the automorphism group of a binary self-dual $$[120, 60, 24]$$ [ 120 , 60 , 24 ] code" @default.
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- W2950184777 doi "https://doi.org/10.1007/s00200-013-0193-0" @default.
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