New extremal singly even self-dual codes of lengths $64$ and $66$

Abstract

For lengths $64$ and $66$, we construct extremal singly even self-dual codes with weight enumerators for which no extremal singly even self-dual codes were previously known to exist. We also construct new $40$ inequivalent extremal doubly even self-dual $[64,32,12]$ codes with covering radius $12$ meeting the Delsarte bound.

13 pages. arXiv admin note: text overlap with arXiv:1706.01694

References in corpus (2)

• New extremal binary self-dual codes from F_4 + uF_4-lifts of quadratic double circulant codes over F_4
• New cubic self-dual codes of length 54, 60 and 66

Cited by in corpus (4)

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• New binary self-dual codes via a generalization of the four circulant construction
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• On the existence of $s$-extremal singly even self-dual codes