Please use this identifier to cite or link to this item:
Title: Abelian codes in principal ideal group algebras
Authors: Jitman, Somphong
Ling, San
Liu, Hongwei
Xie, Xiaoli
Keywords: DRNTU::Science::Mathematics::Applied mathematics::Information theory
Issue Date: 2013
Source: Jitman, S., Ling, S., Liu, H., & Xie, X. (2013). Abelian Codes in Principal Ideal Group Algebras. IEEE Transactions on Information Theory, 59(5), 3046-3058.
Series/Report no.: IEEE transactions on information theory
Abstract: We 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.
ISSN: 0018-9448
DOI: 10.1109/TIT.2012.2236383
Schools: School of Physical and Mathematical Sciences 
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:SPMS Journal Articles

Citations 10

Updated on May 27, 2023

Web of ScienceTM
Citations 10

Updated on May 26, 2023

Page view(s) 10

Updated on May 29, 2023

Google ScholarTM




Items in DR-NTU are protected by copyright, with all rights reserved, unless otherwise indicated.