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

Year 2018, Volume: 5 Issue: 3, 143 - 151, 08.10.2018

Damyan Anev Masaaki Harada Nikolay Yankov

https://doi.org/10.13069/jacodesmath.458601

Cited By: 8

Abstract

For lengths $64$ and $66$,
we construct six and seven extremal singly even self-dual
codes with weight enumerators for which no extremal
singly even self-dual codes were previously known to exist, respectively.
We also construct new $40$ inequivalent
extremal doubly even self-dual $[64,32,12]$ codes
with covering radius $12$ meeting the Delsarte bound.
These new codes are constructed by considering
four-circulant codes along with their neighbors and shadows.

Keywords

Self-dual code, Weight enumerator

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