Group codes of dimension 2 and 3 are abelian

Garcia Pillado C.; Gonzalez S.; Markov V; Markova O.; Martinez C.

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Group codes of dimension 2 and 3 are abelian

机译：维度2和3的组代码是阿贝尔语

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摘要

Let F be a finite field and let G be a finite group. We show that if C is a G-code over F with dim(F)(C) = 3 then C is an abelian group code. Since there exist non-abelian group codes of dimension 4 when char F 2 (see the examples in [1]), we conclude that the smallest dimension of a non-abelian group code over a finite field is 4. Published by Elsevier Inc.

机译：令F为有限域，令G为有限群。我们证明，如果C是在F上的G代码，且dim（F）（C）<= 3，则C是阿贝尔群代码。由于当char F> 2时存在维度为4的非阿贝尔群代码（请参见[1]中的示例），因此我们得出结论，非阿贝尔群代码在有限域上的最小维数为4。由Elsevier Inc发布。

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来源
《Finite fields and their applications》 |2019年第1期|167-176|共10页
作者
Garcia Pillado C.; Gonzalez S.; Markov V; Markova O.; Martinez C.;
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作者单位

Univ Oviedo, Dept Math, Oviedo, Spain;

Univ Oviedo, Dept Math, Oviedo, Spain;

Moscow MV Lomonosov State Univ, Dept Mech & Math, Moscow, Russia;

Moscow MV Lomonosov State Univ, Dept Mech & Math, Moscow, Russia;

Univ Oviedo, Dept Math, Oviedo, Spain;

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正文语种 eng
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关键词
Group code; Abelian group code;

机译：组码;阿贝尔组码;

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Group codes of dimension 2 and 3 are abelian

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