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...
Saved in:
| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2003 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2003
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/155694 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-155694 |
|---|---|
| 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 |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
On check character systems over quasigroups and loops |
| spellingShingle |
On check character systems over quasigroups and loops Belyavskaya, G.B. |
| 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 |
| author |
Belyavskaya, G.B. |
| author_facet |
Belyavskaya, G.B. |
| publishDate |
2003 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| 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.
|
| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.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. |
| work_keys_str_mv |
AT belyavskayagb oncheckcharactersystemsoverquasigroupsandloops |
| first_indexed |
2025-12-07T17:36:12Z |
| last_indexed |
2025-12-07T17:36:12Z |
| _version_ |
1850871877203918848 |