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...
Gespeichert in:
| Veröffentlicht in: | Algebra and Discrete Mathematics |
|---|---|
| Datum: | 2009 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут прикладної математики і механіки НАН України
2009
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/154622 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862731841937604608 |
|---|---|
| author | Dutra, F.S. Ferraz, R.A. Milies, C.P. |
| author_facet | Dutra, F.S. Ferraz, R.A. Milies, C.P. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
|
| first_indexed | 2025-12-07T19:28:21Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-154622 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T19:28:21Z |
| publishDate | 2009 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | Semisimple group codes and dihedral codes Dutra, F.S. Ferraz, R.A. Milies, C.P. |
| title | 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_short | Semisimple group codes and dihedral codes |
| title_sort | semisimple group codes and dihedral codes |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/154622 |
| work_keys_str_mv | AT dutrafs semisimplegroupcodesanddihedralcodes AT ferrazra semisimplegroupcodesanddihedralcodes AT miliescp semisimplegroupcodesanddihedralcodes |