Abelian codes in principal ideal group algebras

• Main Authors: Jitman, Somphong, Ling, San, Liu, Hongwei, Xie, Xiaoli
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2013
• Subjects: DRNTU::Science::Mathematics::Applied mathematics::Information theory
• Online Access: https://hdl.handle.net/10356/107232; http://hdl.handle.net/10220/17834; http://dx.doi.org/10.1109/TIT.2012.2236383
• Institution: Nanyang Technological University

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 eve...