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

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.Comment: 23 pages, 6 tables, to appear in Finite Fields and Their Application

Classification of quaternary Hermitian self-dual codes of length 20

A classification of quaternary Hermitian self-dual codes of length 20 is given. Using this classification, a classification of extremal quaternary Hermitian self-dual codes of length 22 is also given.Comment: 9 pages. To appear in IEEE Transactions on Information Theor