Naoki Chigira

Extremal self-dual codes of length 64 through neighbors and covering radii

We construct extremal singly even self-dual [64,32,12] codes with weight enumerators which were not known to be attainable. In particular, we find some codes whose shadows have minimum weight 12. By considering their doubly even neighbors, extremal doubly even self-dual [64,32,12] codes with covering radius 12 are constructed for the first time.

Self-Dual Codes Related to the Rudvalis Group

In this note, we will show that there exist exactly three self-dual codes with the automorphism group isomorphic to the Rudvalis group up to equivalence. Furthermore we will give some descriptions of codewords which span these codes. Especially, we will describe some codewords by using a relation between the rank 3 graph of the Rudvalis group and the Hoffman–Singleton graph.

On the classification of extremal doubly even self-dual codes with 2-transitive automorphism groups

In this note, we complete the classification of extremal doubly even self-dual codes with 2-transitive automorphism groups.

On Involutions Which Generate Mathieu Groups M 11 and M 12

Abstract We will give an elementary construction of the Mathieu groups M 11 and M 12.