Semisimple group codes and dihedral codes
We consider codes that are given as two-sided ideals in a semisimple finite group algebra FqG 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-sided ideals o f FqG...
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| Datum: | 2009 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут прикладної математики і механіки НАН України
2009
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| Schriftenreihe: | Algebra and Discrete Mathematics |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/154622 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Semisimple group codes and dihedral codes/ F.S. Dutra, R.A. Ferraz, C.P. Milies // Algebra and Discrete Mathematics. — 2009. — Vol. 8, № 3. — С. 28–48. — Бібліогр.: 12 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | We consider codes that are given as two-sided ideals in a semisimple finite group algebra FqG 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-sided ideals o f FqG in the case when G is a dihedral group and extend these results also to a family of quaternion group codes. In the final sectio n, we give a method of decoding; i.e., of finding and correcting eve ntual transmission errors. |
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