On $s$-extremal singly even self-dual $[24k+8,12k+4,4k+2]$ codes

Abstract

A relationship between $s$-extremal singly even self-dual $[24k+8,12k+4,4k+2]$ codes and extremal doubly even self-dual $[24k+8,12k+4,4k+4]$ codes with covering radius meeting the Delsarte bound, is established. As an example of the relationship, $s$-extremal singly even self-dual $[56,28,10]$ codes are constructed for the first time. In addition, we show that there is no extremal doubly even self-dual code of length $24k+8$ with covering radius meeting the Delsarte bound for $k\ge 137$. Similarly, we show that there is no extremal doubly even self-dual code of length $24k+16$ with covering radius meeting the Delsarte bound for $k\ge 148$.

15 pages, minor revision

References in corpus (2)

• New extremal binary self-dual codes from a modified four circulant construction
• Extension theorems for self-dual codes over rings and new binary self-dual codes

Cited by in corpus (2)

• On the existence of $s$-extremal singly even self-dual codes
• Singly even self-dual codes of length $24k+10$ and minimum weight $4k+2$