Ontology type: schema:ScholarlyArticle
2012-10
AUTHORSC. García Pillado, S. González, V. T. Markov, C. Martínez, A. A. Nechaev
ABSTRACTLet 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| ∉ {24, 48, 54, 60, 64, 72, 96, 108, 120}, but for F = and G = S4 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. More... »
PAGES578-585
http://scigraph.springernature.com/pub.10.1007/s10958-012-1006-x
DOIhttp://dx.doi.org/10.1007/s10958-012-1006-x
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