New extremal singly even self-dual codes of lengths 6464 and 6666

For lengths $64$ and $66$, we construct extremal singly even self-dual codes with weight enumerators for which no extremal singly even self-dual codes were previously known to exist. We also construct new $40$ inequivalent extremal doubly even self-dual $[64,32,12]$ codes with covering radius $12$ meeting the Delsarte bound.Comment: 13 pages. arXiv admin note: text overlap with arXiv:1706.0169

Some restrictions on weight enumerators of singly even self-dual codes II

In this note, we give some restrictions on the number of vectors of weight $d/2+1$ in the shadow of a singly even self-dual $[n,n/2,d]$ code. This eliminates some of the possible weight enumerators of singly even self-dual $[n,n/2,d]$ codes for $(n,d)=(62,12)$, $(72,14)$, $(82,16)$, $(90,16)$ and $(100,18)$.Comment: 16 page