On check character systems over quasigroups and loops
In this article we study check character systems that is error detecting codes, which arise by appending a check digit an to every word a₁a₂...an₋₁ : a₁a₂...an₋₁ → a₁a₂...an₋₁an with the check formula (...((a₁ · δa₂) · δ ²a₃)...) · δ ⁿ⁻²an₋₁) · δ ⁿ⁻¹an = c, where Q(·) is a quasigroup or a loop, δ is...
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| Опубліковано в: : | Algebra and Discrete Mathematics |
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| Дата: | 2003 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2003
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/155694 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On check character systems over quasigroups and loops / G.B. Belyavskaya // Algebra and Discrete Mathematics. — 2003. — Vol. 2, № 2. — С. 1–13. — Бібліогр.: 9 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862712231735590912 |
|---|---|
| author | Belyavskaya, G.B. |
| author_facet | Belyavskaya, G.B. |
| citation_txt | On check character systems over quasigroups and loops / G.B. Belyavskaya // Algebra and Discrete Mathematics. — 2003. — Vol. 2, № 2. — С. 1–13. — Бібліогр.: 9 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | In this article we study check character systems that is error detecting codes, which arise by appending a check digit an to every word a₁a₂...an₋₁ : a₁a₂...an₋₁ → a₁a₂...an₋₁an with the check formula (...((a₁ · δa₂) · δ ²a₃)...) · δ ⁿ⁻²an₋₁) · δ ⁿ⁻¹an = c, where Q(·) is a quasigroup or a loop, δ is a permutation of Q, c ∈ Q. We consider detection sets for such errors as transpositions (ab → ba), jump transpositions (acb → bca), twin errors (aa → bb) and jump twin errors (aca → bcb) and an automorphism equivalence (a weak equivalence) for a check character systems over the same quasigroup (over the same loop). Such equivalent systems detect the same percentage (rate) of the considered error types.
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| first_indexed | 2025-12-07T17:36:12Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-155694 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T17:36:12Z |
| publishDate | 2003 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Belyavskaya, G.B. 2019-06-17T10:47:49Z 2019-06-17T10:47:49Z 2003 On check character systems over quasigroups and loops / G.B. Belyavskaya // Algebra and Discrete Mathematics. — 2003. — Vol. 2, № 2. — С. 1–13. — Бібліогр.: 9 назв. — англ. 1726-3255 2001 Mathematics Subject Classification: 20N05, 20N15, 94B60, 94B65. https://nasplib.isofts.kiev.ua/handle/123456789/155694 In this article we study check character systems that is error detecting codes, which arise by appending a check digit an to every word a₁a₂...an₋₁ : a₁a₂...an₋₁ → a₁a₂...an₋₁an with the check formula (...((a₁ · δa₂) · δ ²a₃)...) · δ ⁿ⁻²an₋₁) · δ ⁿ⁻¹an = c, where Q(·) is a quasigroup or a loop, δ is a permutation of Q, c ∈ Q. We consider detection sets for such errors as transpositions (ab → ba), jump transpositions (acb → bca), twin errors (aa → bb) and jump twin errors (aca → bcb) and an automorphism equivalence (a weak equivalence) for a check character systems over the same quasigroup (over the same loop). Such equivalent systems detect the same percentage (rate) of the considered error types. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On check character systems over quasigroups and loops Article published earlier |
| spellingShingle | On check character systems over quasigroups and loops Belyavskaya, G.B. |
| title | On check character systems over quasigroups and loops |
| title_full | On check character systems over quasigroups and loops |
| title_fullStr | On check character systems over quasigroups and loops |
| title_full_unstemmed | On check character systems over quasigroups and loops |
| title_short | On check character systems over quasigroups and loops |
| title_sort | on check character systems over quasigroups and loops |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/155694 |
| work_keys_str_mv | AT belyavskayagb oncheckcharactersystemsoverquasigroupsandloops |