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arXiv · 2004.03396

A note on the Assmus--Mattson theorem for some binary codes

Tsuyoshi Miezaki·Hiroyuki Nakasora
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Abstract

We previously proposed the first nontrivial examples of a code having support $t$-designs for all weights obtained from the Assmus-Mattson theorem and having support $t'$-designs for some weights with some $t'>t$. This suggests the possibility of generalizing the Assmus-Mattson theorem, which is very important in design and coding theory. In the present paper, we generalize this example as a strengthening of the Assmus-Mattson theorem along this direction. As a corollary, we provide a new characterization of the extended Golay code $\mathcal{G}_{24}$.

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Tsuyoshi Miezaki, Hiroyuki Nakasora. 2020-04-06. A note on the Assmus--Mattson theorem for some binary codes. https://arxiv.org/abs/2004.03396

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