Tsuyoshi Miezaki, Hiroyuki Nakasora
Published 2020-04-06Version 1
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 G_24.
Comments: 19 pages. arXiv admin note: text overlap with arXiv:1805.10019
A note on the Assmus--Mattson theorem for some binary codes II
A note on the Assmus--Mattson theorem for some non-binary codes (a resume)
$t$-designs obtained from two shells and exceptional examples of them
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