JP Journal of Algebra, Number Theory and Applications
Volume 45, Issue 1, Pages 13 - 28
(January 2020) http://dx.doi.org/10.17654/NT045010013 |
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COMPUTING THE DIMENSION OF IDEALS IN GROUP ALGEBRAS, WITH AN APPLICATION TO CODING THEORY
Michele Elia and Elisa Gorla
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Abstract: The problem of computing the dimension of a left/right ideal in a group algebra of a finite group over a field is considered. The ideal dimension is related to the rank of a matrix originating from a regular left/right representation of in particular, when 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. |
Keywords and phrases: group algebra, ideal, group code, representation, rank, characteristic polynomial.
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