On the classification of the extremal self-dual codes over small fields with 2-transitive automorphism groups

Anton Malevich; Wolfgang Willems

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On the classification of the extremal self-dual codes over small fields with 2-transitive automorphism groups

机译：具有2个传递自同构群的小场上的极值自对偶码的分类

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摘要

There are seven binary extremal self-dual doubly-even codes which are known to have a 2-transitive automorphism group. Using representation theoretical methods we show that there are no other such codes, except possibly for length n = 1024. We also classify all extremal ternary self-dual and quaternary Hermitian self-dual codes.

机译：存在七个已知具有2个传递自同构群的二进制极值自对偶双偶码。使用表示理论方法，我们表明除长度n = 1024之外，没有其他此类代码。我们还对所有极值三元自对偶和四元Hermitian自对偶代码进行分类。

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来源
《Designs, Codes and Crytography》 |2014年第2期|69-76|共8页
作者
Anton Malevich; Wolfgang Willems;
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作者单位

Department of Mathematics, Otto-von-Guericke University Magdeburg, 39016 Magdeburg. Germany;

Department of Mathematics, Otto-von-Guericke University Magdeburg, 39016 Magdeburg, Germany;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Automorphisms; Self-dual codes; Transitive groups; Simple groups;

机译：自同构;自对码;传递组;简单组;

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1. On the classification of extremal doubly even self-dual codes with 2-transitive automorphism groups [J] . Naoki Chigira, Masaaki Harada, Masaaki Kitazume Designs, Codes and Crytography . 2014,第1期

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2. Corrigendum to "Construction of extremal self-dual codes over F_2 + uF_2 with an automorphism of odd order" [Finite Fields Appl. 18 (2012) 971-992] [J] . Hyun Jin Kim, Yoonjin Lee Finite fields and their applications . 2013,第sepa期

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3. Self-dual codes with an automorphism of order 7 and s-extremal codes of length 68 [J] . Yankov Nikolay, Ivanova Milena, Lee Moon Ho Finite fields and their applications . 2018,第MAY期

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4. Classification of circulant and 4-circulant extremal additive self-dual codes [C] . T. Aaron Gulliver, Jon-Lark Kim IEEE International Symposium on Information Theory . 2002

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5. Existence of certain extremal self-dual codes. [D] . Tsai, Han-Ping. 1992

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机译：关于极值偶偶自编码的分类 2-传递自同构群

On the classification of the extremal self-dual codes over small fields with 2-transitive automorphism groups

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