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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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Інститут прикладної математики і механіки НАН України
2003
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| Series: | Algebra and Discrete Mathematics |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/155694 |
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irk-123456789-1556942019-06-18T01:28:12Z On check character systems over quasigroups and loops Belyavskaya, G.B. 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. 2003 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/155694 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
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English |
| 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. |
| format |
Article |
| author |
Belyavskaya, G.B. |
| spellingShingle |
Belyavskaya, G.B. On check character systems over quasigroups and loops Algebra and Discrete Mathematics |
| author_facet |
Belyavskaya, G.B. |
| author_sort |
Belyavskaya, G.B. |
| title |
On check character systems over quasigroups and loops |
| title_short |
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_sort |
on check character systems over quasigroups and loops |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2003 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/155694 |
| 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. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT belyavskayagb oncheckcharactersystemsoverquasigroupsandloops |
| first_indexed |
2023-05-20T17:46:47Z |
| last_indexed |
2023-05-20T17:46:47Z |
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1796154077231448064 |