Self-dual codes over $\mathbb{F}_5$ and $s$-extremal unimodular lattices

Masaaki Harada

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arXiv · 2208.03617

Self-dual codes over $\mathbb{F}_5$ and $s$-extremal unimodular lattices

Masaaki Harada

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Abstract

New $s$-extremal extremal unimodular lattices in dimensions $38$, $40$, $42$ and $44$ are constructed from self-dual codes over $\mathbb{F}_5$ by Construction A. In the process of constructing these codes, we obtain a self-dual $[44,22,14]$ code over $\mathbb{F}_5$. In addition, the code implies a $[43,22,13]$ code over $\mathbb{F}_5$. These codes have larger minimum weights than the previously known $[44,22]$ codes and $[43,22]$ codes, respectively.

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Masaaki Harada. 2022-08-07. Self-dual codes over $\mathbb{F}_5$ and $s$-extremal unimodular lattices. https://arxiv.org/abs/2208.03617

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