Computing the dimension of ideals in group algebras, with an application to coding theory

Michele Elia; Elisa Gorla

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arXiv · 1403.7920

Computing the dimension of ideals in group algebras, with an application to coding theory

Michele Elia·Elisa Gorla

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Abstract

The problem of computing the dimension of a left/right ideal in a group algebra F[G] of a finite group G over a field F is considered. The ideal dimension is related to the rank of a matrix originating from a regular left/right representation of G; in particular, when F[G] is semisimple, the dimension of a principal ideal is equal to the rank of the matrix representing a generator. From this observation, a bound and an efficient algorithm to compute the dimension of an ideal in a group ring are established. Since group codes are ideals in finite group rings, the algorithm allows efficient computation of their dimension.

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Michele Elia, Elisa Gorla. 2014-03-31. Computing the dimension of ideals in group algebras, with an application to coding theory. https://arxiv.org/abs/1403.7920

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