Линейные и групповые совершенные коды над телами и квазителами Full article
| Journal |
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports)
, E-ISSN: 1813-3304 |
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| Output data | Year: 2023, Volume: 20, Number: 2, Pages: 1093-1107 Pages count : 15 DOI: 10.33048/semi.2023.20.068 | ||
| Tags | skew eld, quasi skew eld, perfect code, checking matrix, quaternions, octonions | ||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Russian Science Foundation | 22-11-00266 |
Abstract:
In this paper, we propose a general construction of linear perfect codes over innite skew elds and quasi skew elds with right (left) unity. A complete classi cation of such codes over associative skew elds is given. Since the cardinality of the considered skew elds is innite, the constructed codes have an innite length. In the previous work, we considered codes over innite countable elds, the length of which was also countable. We now remove this restriction and assume that the cardinality of the skew eld and the length of the codes can be arbitrary (not necessarily countable).
Cite:
Малюгин С.А.
Линейные и групповые совершенные коды над телами и квазителами
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2023. Т.20. №2. С.1093-1107. DOI: 10.33048/semi.2023.20.068 WOS Scopus РИНЦ
Линейные и групповые совершенные коды над телами и квазителами
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2023. Т.20. №2. С.1093-1107. DOI: 10.33048/semi.2023.20.068 WOS Scopus РИНЦ
Dates:
| Submitted: | Apr 25, 2023 |
| Published print: | Nov 23, 2023 |
| Published online: | Nov 23, 2023 |
Identifiers:
| Web of science: | WOS:001164415100001 |
| Scopus: | 2-s2.0-85179734783 |
| Elibrary: | 82134654 |
Citing:
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