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dc.contributor.author |
Belyavskaya, G.B. |
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dc.date.accessioned |
2019-06-17T10:47:49Z |
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dc.date.available |
2019-06-17T10:47:49Z |
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dc.date.issued |
2003 |
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dc.identifier.citation |
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. |
uk_UA |
dc.identifier.issn |
1726-3255 |
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dc.identifier.other |
2001 Mathematics Subject Classification: 20N05, 20N15, 94B60, 94B65. |
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dc.identifier.uri |
http://dspace.nbuv.gov.ua/handle/123456789/155694 |
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dc.description.abstract |
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. |
uk_UA |
dc.language.iso |
en |
uk_UA |
dc.publisher |
Інститут прикладної математики і механіки НАН України |
uk_UA |
dc.relation.ispartof |
Algebra and Discrete Mathematics |
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dc.title |
On check character systems over quasigroups and loops |
uk_UA |
dc.type |
Article |
uk_UA |
dc.status |
published earlier |
uk_UA |
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