Abstract
We present an intrinsecal characterization of when a linear code C is a (left) group code, i.e. the ambient space can be identified with a group algebra in which the standard basis is the group basis such that C is a (left) ideal in this group algebra. As application we obtain a class containing properly the class of metacyclic groups such that every group code is an abelian group code. We also use the characterization to describe all the possible group structures on some classes of generalized Reed-Solomon codes.
Research supported by D.G.I. of Spain and Fundación Séneca of Murcia.
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Bernal, J.J., del Río, Á., Simón, J.J. (2008). How to Know if a Linear Code Is a Group Code?. In: Barbero, Á. (eds) Coding Theory and Applications. Lecture Notes in Computer Science, vol 5228. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87448-5_4
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DOI: https://doi.org/10.1007/978-3-540-87448-5_4
Publisher Name: Springer, Berlin, Heidelberg
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