Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8895679 | Finite Fields and Their Applications | 2018 | 18 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Martino Borello, Javier de la Cruz,