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).
