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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Veröffentlicht in:Algebra and Discrete Mathematics
Datum:2003
1. Verfasser: Belyavskaya, G.B.
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут прикладної математики і механіки НАН України 2003
Online Zugang: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
Zitieren: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.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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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.
first_indexed 2025-12-07T17:36:12Z
format Article
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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