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

## TL;DR

This paper establishes restrictions on the number of vectors of a specific weight in the shadow of singly even self-dual codes, narrowing down possible weight enumerators for certain code parameters.

## Contribution

It introduces new restrictions on vector counts in the shadow of singly even self-dual codes, eliminating some potential weight enumerators for specific code lengths and minimum distances.

## Key findings

- Eliminates some possible weight enumerators for codes with parameters (62,12), (72,14), (82,16), (90,16), (100,18)
- Provides restrictions on the number of vectors of weight d/2+1 in the shadow
- Narrows the classification of singly even self-dual codes based on weight enumerators

## Abstract

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 $(100,18)$.