Group codes of dimension 2 and 3 are abelian.

Finite Fields and Their Applications(2019)

Cited 9|Views14
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Abstract
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 dimF⁡(C)≤3 then C is an abelian group code. Since there exist non-abelian group codes of dimension 4 when charF>2 (see the examples in [1]), we conclude that the smallest dimension of a non-abelian group code over a finite field is 4.
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94B05,94B60
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