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Article Dans Une Revue Finite Fields and Their Applications Année : 2018

Some new results on the self-dual [120,60,24] code

Résumé

The existence of an extremal self-dual binary linear code of length 120 is a long-standing open problem. We continue the investigation of its automorphism group, proving that automorphisms of order 30 and 57 cannot occur. Supposing the involutions acting fixed point freely, we show that also automorphisms of order 8 cannot occur and the automorphism group is of order at most 120, with further restrictions. Finally, we present some necessary conditions for the existence of the code, based on shadow and design theory.
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Dates et versions

hal-03852299 , version 1 (14-11-2022)

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Martino Borello, Javier de la Cruz. Some new results on the self-dual [120,60,24] code. Finite Fields and Their Applications, 2018, 50, pp.17-34. ⟨10.1016/j.ffa.2017.11.004⟩. ⟨hal-03852299⟩
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