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On check character systems over quasigroups and loops

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 \(a_n\) to every word \(a_1a_2...a_{n-1}: a_1a_2...a_{n-1} \rightarrow a_1a_2...a_{n-1}a_n\) with the check formula \( (...((a_1\cdot \delta a_2)\cdot \delta^2a_3)...)\cdot \delta^{...

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Bibliographic Details
Main Author: Belyavskaya, G. B.
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2018
Subjects:
quasigroup
loop
group
automorphism
check character system
code
20N05
20N15
94B60
94B65
Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/955
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spelling oai:ojs.admjournal.luguniv.edu.ua:article-9552018-05-13T07:14:40Z On check character systems over quasigroups and loops Belyavskaya, G. B. quasigroup, loop, group, automorphism, check character system, code 20N05, 20N15, 94B60, 94B65 In this article we study check character systems that is error detecting codes, which arise by appending a check digit \(a_n\) to every word \(a_1a_2...a_{n-1}: a_1a_2...a_{n-1} \rightarrow a_1a_2...a_{n-1}a_n\) with the check formula \( (...((a_1\cdot \delta a_2)\cdot \delta^2a_3)...)\cdot \delta^{n-2}a_{n-1})\cdot\delta^{n-1}a_n = c\), where \(Q(\cdot)\) is a quasigroup or a loop, \(\delta\) is a permutation of \(Q\), \(c \in Q\). We consider detection sets for such errors as transpositions (\(ab \rightarrow ba\)), jump transpositions (\(acb \rightarrow bca\)), twin errors (\(aa \rightarrow bb\)) and jump twin errors (\(aca \rightarrow bcb\)) 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. Lugansk National Taras Shevchenko University 2018-05-13 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/955 Algebra and Discrete Mathematics; Vol 2, No 2 (2003) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/955/484 Copyright (c) 2018 Algebra and Discrete Mathematics
institution Algebra and Discrete Mathematics
collection OJS
language English
topic quasigroup
loop
group
automorphism
check character system
code
20N05
20N15
94B60
94B65
spellingShingle quasigroup
loop
group
automorphism
check character system
code
20N05
20N15
94B60
94B65
Belyavskaya, G. B.
On check character systems over quasigroups and loops
topic_facet quasigroup
loop
group
automorphism
check character system
code
20N05
20N15
94B60
94B65
format Article
author Belyavskaya, G. B.
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
description In this article we study check character systems that is error detecting codes, which arise by appending a check digit \(a_n\) to every word \(a_1a_2...a_{n-1}: a_1a_2...a_{n-1} \rightarrow a_1a_2...a_{n-1}a_n\) with the check formula \( (...((a_1\cdot \delta a_2)\cdot \delta^2a_3)...)\cdot \delta^{n-2}a_{n-1})\cdot\delta^{n-1}a_n = c\), where \(Q(\cdot)\) is a quasigroup or a loop, \(\delta\) is a permutation of \(Q\), \(c \in Q\). We consider detection sets for such errors as transpositions (\(ab \rightarrow ba\)), jump transpositions (\(acb \rightarrow bca\)), twin errors (\(aa \rightarrow bb\)) and jump twin errors (\(aca \rightarrow bcb\)) 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.
publisher Lugansk National Taras Shevchenko University
publishDate 2018
url https://admjournal.luguniv.edu.ua/index.php/adm/article/view/955
work_keys_str_mv AT belyavskayagb oncheckcharactersystemsoverquasigroupsandloops
first_indexed 2024-04-12T06:25:56Z
last_indexed 2024-04-12T06:25:56Z
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