Singly-even self-dual codes with minimal shadow

TL;DR

This paper studies extremal singly-even self-dual codes with minimal shadow, establishing bounds and proving non-existence for certain parameters, thereby advancing understanding of their structural limitations.

Contribution

It provides explicit bounds on the length of such codes with minimal shadow and proves their non-existence for specific parameters, extending previous theoretical results.

Findings

Bounded the length of extremal singly-even self-dual codes with minimal shadow

Proved non-existence of such codes for certain parameters

Extended theoretical understanding of code structure and limitations

Abstract

In this note we investigate extremal singly-even self-dual codes with minimal shadow. For particular parameters we prove non-existence of such codes. By a result of Rains \cite{Rains-asymptotic}, the length of extremal singly-even self-dual codes is bounded. We give explicit bounds in case the shadow is minimal.