Construction of extremal Type II $\mathbb{Z}_{2k}$-codes

Masaaki Harada

doi:10.1016/j.ffa.2022.102154

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arXiv · 2201.01439

Construction of extremal Type II $\mathbb{Z}_{2k}$-codes

Masaaki Harada

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Abstract

We give methods for constructing many self-dual $\mathbb{Z}_m$-codes and Type II $\mathbb{Z}_{2k}$-codes of length $2n$ starting from a given self-dual $\mathbb{Z}_m$-code and Type II $\mathbb{Z}_{2k}$-code of length $2n$, respectively. As an application, we construct extremal Type II $\mathbb{Z}_{2k}$-codes of length $24$ for $k=4,5,\ldots,20$ and extremal Type II $\mathbb{Z}_{2k}$-codes of length $32$ for $k=4,5,\ldots,10$. We also construct new extremal Type II $\mathbb{Z}_4$-codes of lengths $56$ and $64$.

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Masaaki Harada. 2022-01-05. Construction of extremal Type II $\mathbb{Z}_{2k}$-codes. https://doi.org/10.1016/j.ffa.2022.102154

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