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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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2009 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут прикладної математики і механіки НАН України
2009
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| Online Zugang: | https://nasplib.isofts.kiev.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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Dutra, F.S. Ferraz, R.A. Milies, C.P. 2019-06-15T16:58:39Z 2019-06-15T16:58:39Z 2009 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. 1726-3255 2000 Mathematics Subject Classification:94B15, 94B60, 16S34, 20C05. https://nasplib.isofts.kiev.ua/handle/123456789/154622 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. Research supported by FAPESP, Procs. 02/02933-0 and 00/07291-0 and CNPqProc. 300243/79-0 (RN) en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Semisimple group codes and dihedral codes Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Semisimple group codes and dihedral codes |
| spellingShingle |
Semisimple group codes and dihedral codes Dutra, F.S. Ferraz, R.A. Milies, C.P. |
| title_short |
Semisimple group codes and dihedral codes |
| title_full |
Semisimple group codes and dihedral codes |
| title_fullStr |
Semisimple group codes and dihedral codes |
| title_full_unstemmed |
Semisimple group codes and dihedral codes |
| title_sort |
semisimple group codes and dihedral codes |
| author |
Dutra, F.S. Ferraz, R.A. Milies, C.P. |
| author_facet |
Dutra, F.S. Ferraz, R.A. Milies, C.P. |
| publishDate |
2009 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| description |
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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| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/154622 |
| citation_txt |
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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AT dutrafs semisimplegroupcodesanddihedralcodes AT ferrazra semisimplegroupcodesanddihedralcodes AT miliescp semisimplegroupcodesanddihedralcodes |
| first_indexed |
2025-12-07T19:28:21Z |
| last_indexed |
2025-12-07T19:28:21Z |
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1850878933301460992 |