Geodesic
When are all group codes of a~noncommutative group Abelian (a~computational approach)?
Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 2, pp. 75-85.

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Let $G$ be a finite group and $F$ be a field. Any linear code over $F$ that is permutation equivalent to some code defined by an ideal of the group ring $FG$ will be called a $G$-code. The theory of these “abstract” group codes was developed in 2009. A code is called Abelian if it is an $A$-code for some Abelian group $A$. Some conditions were given that all $G$-codes for some group $G$ are Abelian but no examples of non-Abelian group codes were known at that time. We use a computer algebra system GAP to show that all $G$-codes over any field are Abelian if $|G|128$ and $|G|\notin\{24,48,54,60,64,72,96,108,120\}$, but for $F=\mathbb F_5$ and $G=\mathrm S_4$ there exist non-Abelian $G$-codes over $F$. It is also shown that the existence of left non-Abelian group codes for a given group depends in general on the field of coefficients, while for (two-sided) group codes the corresponding question remains open. 
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     title = {When are all group codes of a~noncommutative group {Abelian} (a~computational approach)?},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
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C. García Pillado; S. González; V. T. Markov; C. Martínez; A. A. Nechaev. When are all group codes of a~noncommutative group Abelian (a~computational approach)?. Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 2, pp. 75-85. http://geodesic.mathdoc.fr/item/FPM_2012_17_2_a1/

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