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Self-dual codes over $\mathbb{F}_5$ and $s$-extremal unimodular lattices (2208.03617v1)
Published 7 Aug 2022 in cs.IT, math.CO, math.IT, and math.NT
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.