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arXiv · 1511.02972

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

Masaaki Harada·Akihiro Munemasa
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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 $k \ge 148$.

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Masaaki Harada, Akihiro Munemasa. 2017-07-21. On $s$-extremal singly even self-dual $[24k+8,12k+4,4k+2]$ codes. https://doi.org/10.1016/j.ffa.2017.08.008

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