Semisimple group codes and dihedral codes

• Datum: 2018
• Hauptverfasser: Dutra, Flaviana S., Ferraz, Raul A., Milies, C. Polcino
• Format: Artikel
• Sprache: English
• Veröffentlicht: Lugansk National Taras Shevchenko University 2018
• Schlagworte: group code; minimal code; group algebra; idempotent; dihedral group; quaternion group; 94B15; 94B60; 16S34; 20C05
• Online Zugang: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/785
• Назва журналу: Algebra and Discrete Mathematics

We consider codes that are given as two-sided ideals in a semisimple finite group algebra \({\mathbb F}_q G\)  defined by idempotents constructed from subgroups of \(G\) in a natural way and compute their dimensions and weights. We give a criterion to decide when these ideals are all the minimal two...