Binary extremal self-dual codes of length $60$ and related codes

Abstract

We give a classification of four-circulant singly even self-dual $[60,30,d]$ codes for $d=10$ and $12$. These codes are used to construct extremal singly even self-dual $[60,30,12]$ codes with weight enumerator for which no extremal singly even self-dual code was previously known to exist. From extremal singly even self-dual $[60,30,12]$ codes, we also construct extremal singly even self-dual $[58,29,10]$ codes with weight enumerator for which no extremal singly even self-dual code was previously known to exist. Finally, we give some restriction on the possible weight enumerators of certain singly even self-dual codes with shadow of minimum weight $1$.

13 pages

References in corpus (1)

• New extremal binary self-dual codes from F_4 + uF_4-lifts of quadratic double circulant codes over F_4

Cited by in corpus (3)

• New binary self-dual codes of lengths 56, 58, 64, 80 and 92 from a modification of the four circulant construction
• On the existence of $s$-extremal singly even self-dual codes
• Singly even self-dual codes of length $24k+10$ and minimum weight $4k+2$