dc.contributor.authorJitman, Somphong
dc.contributor.authorLing, San
dc.contributor.authorLiu, Hongwei
dc.contributor.authorXie, Xiaoli
dc.identifier.citationJitman, S., Ling, S., Liu, H., & Xie, X. (2013). Abelian Codes in Principal Ideal Group Algebras. IEEE Transactions on Information Theory, 59(5), 3046-3058.en_US
dc.description.abstractWe study abelian codes in principal ideal group algebras (PIGAs). We first give an algebraic characterization of abelian codes in any group algebra and provide some general results. For abelian codes in a PIGA, which can be viewed as cyclic codes over a semisimple group algebra, it is shown that every abelian code in a PIGA admits generator and check elements. These are analogous to the generator and parity-check polynomials of cyclic codes. A characterization and an enumeration of Euclidean self-dual and Euclidean self-orthogonal abelian codes in a PIGA are given, which generalize recent analogous results for self-dual cyclic codes. In addition, the structures of reversible and complementary dual abelian codes in a PIGA are established, again extending results on reversible and complementary dual cyclic codes. Finally, asymptotic properties of abelian codes in a PIGA are studied. An upper bound for the minimum distance of abelian codes in a non-semisimple PIGA is given in terms of the minimum distance of abelian codes in semisimple group algebras. Abelian codes in a non-semisimple PIGA are then shown to be asymptotically bad, similar to the case of repeated-root cyclic codes.en_US
dc.relation.ispartofseriesIEEE transactions on information theoryen_US
dc.subjectDRNTU::Science::Mathematics::Applied mathematics::Information theory
dc.titleAbelian codes in principal ideal group algebrasen_US
dc.typeJournal Article
dc.contributor.schoolSchool of Physical and Mathematical Sciencesen_US

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