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Designs, Codes and Cryptography

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10-05-2022

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

Authors: Tsuyoshi Miezaki, Hiroyuki Nakasora

Published in: Designs, Codes and Cryptography | Issue 6/2022

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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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Title: A note on the Assmus–Mattson theorem for some binary codes
Authors: Tsuyoshi Miezaki
Hiroyuki Nakasora
Publication date: 10-05-2022
Publisher: Springer US
Published in: Designs, Codes and Cryptography / Issue 6/2022
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-022-01050-2

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