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arXiv 2309.080812023-09math.COcs.ITmath.IT

关于一些三元码的 Assmus--Mattson 定理的一个注记（摘要）

A note on the Assmus--Mattson theorem for some ternary codes (a resume)

Eiichi Bannai, Tsuyoshi Miezaki, Hiroyuki Nakasora

备注：: 6 pages, this is a resume of "A note on the Assmus--Mattson theorem for some ternary codes"

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AI总结：

本文研究二和三重三元码，基于 Assmus--Mattson 定理证明其导出的 $t$-设计满足 $t \leq 5$，并以此给出（扩展）三元 Golay 码的新刻画。

摘要：

设 $C$ 为二和三重三元码。进一步假设由 Assmus--Mattson 定理对所有 $\ell$ 有 $C_\ell$ 均为 $t$-设计。我们证明 $t \leq 5$。作为推论，我们给出（扩展）三元 Golay 码的新刻画。

英文摘要：

Let $C$ be a two and three-weight ternary code. Furthermore, we assume that $C_\ell$ are $t$-designs for all $\ell$ by the Assmus--Mattson theorem. We show that $t \leq 5$. As a corollary, we provide a new characterization of the (extended) ternary Golay code.

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