I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2011/2012, VOLUME 17, NUMBER 2, PAGES 75-85
When are all group codes of a noncommutative group Abelian
(a computational approach)?
C. García Pillado
V. T. Markov
A. A. Nechaev
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a finite group and be a field.
Any linear code over that is permutation
equivalent to some code defined by an ideal of the group ring
called a -code.
The theory of these "abstract" group codes was developed in 2009.
A code is called Abelian if it is an -code for some Abelian
Some conditions were given that all -codes for some
are Abelian but no examples of non-Abelian group codes were known at
We use a computer algebra system GAP to show that all -codes over any field are
Abelian if and , but for
there exist non-Abelian -codes
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.
Last modified: March 6, 2012