A note on the Assmus--Mattson theorem for some binary codes
Combinatorics
2022-04-21 v5 Information Theory
Group Theory
math.IT
Number Theory
Abstract
We previously proposed the first nontrivial examples of a code having support -designs for all weights obtained from the Assmus-Mattson theorem and having support -designs for some weights with some . 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 .
Cite
@article{arxiv.2004.03396,
title = {A note on the Assmus--Mattson theorem for some binary codes},
author = {Tsuyoshi Miezaki and Hiroyuki Nakasora},
journal= {arXiv preprint arXiv:2004.03396},
year = {2022}
}
Comments
21 pages. arXiv admin note: text overlap with arXiv:1805.10019