Abstract

POLCINO MLLIES, César. Group algebras and coding theory: a short survey. Integración - UIS [online]. 2019, vol.37, n.1, pp.153-166. ISSN 0120-419X.  https://doi.org/10.18273/revint.v37n1-2019008..

We study codes constructed from ideals in group algebras and we are particularly interested in their dimensions and weights. First we introduced a special kind of idempotents and study the ideals they generate. We use this information to show that there exist abelian non-cyclic groups that give codes which are more convenient than the cyclic ones. Finally, we discuss briefly some facts about non-abelian codes.

MSC2010: 16S34, 20C05, 94B15.

Keywords : code; Hamming distance; weight; group algebra; ideal; group code.

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