Structure theorems for group ring codes with an application to self-dual codes

Authors
Citation
G. Hughes, Structure theorems for group ring codes with an application to self-dual codes, DES CODES C, 24(1), 2001, pp. 5-14
Citations number
10
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Computer Science & Engineering
Journal title
DESIGNS CODES AND CRYPTOGRAPHY
ISSN journal
0925-1022 → ACNP
Volume
24
Issue
1
Year of publication
2001
Pages
5 - 14
Database
ISI
SICI code
0925-1022(2001)24:1<5:STFGRC>2.0.ZU;2-7
Abstract
Using ideas from the cohomology of finite groups, an isomorphism is establi shed between a group ring and the direct sum of twisted group rings. This g ives a decomposition of a group ring code into twisted group ring codes. In the abelian case the twisted group ring codes are (multi-dimensional) cons tacyclic codes. We use the decomposition to prove that, with respect to the Euclidean inner product, there are no self-dual group ring codes when the group is the direct product of a 2-group and a group of odd order, and the ring is a field of odd characteristic or a certain modular ring. In particu lar, there are no self-dual abelian codes over the rings indicated. Extensi ons of these results to non-Euclidean inner products are briefly discussed.