  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
$(100,18)$.
