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Algebra and Discrete Mathematics, 2003, Issue 2, Pages 1–13
(Mi adm375)
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This article is cited in 2 scientific papers (total in 2 papers)
RESEARCH ARTICLE
On check character systems over quasigroups and loops
G. B. Belyavskaya Institute of Mathematics and Computer, Science, Academy of Sciences of Moldova, str. Academiei, 5, MD–2028, Chishinau, Moldova
Abstract:
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 $a_1a_2\dots a_{n-1}: a_1a_2\dots a_{n-1}\rightarrow a_1a_2\dots a_{n-1}a_n$ with the check formula $ (\dots((a_1\cdot\delta a_2)\cdot \delta^2a_3)\dots)\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.
Keywords:
quasigroup, loop, group, automorphism, check character system, code.
Received: 23.04.2003 Revised: 11.07.2003
Citation:
G. B. Belyavskaya, “On check character systems over quasigroups and loops”, Algebra Discrete Math., 2003, no. 2, 1–13
Linking options:
https://www.mathnet.ru/eng/adm375 https://www.mathnet.ru/eng/adm/y2003/i2/p1
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Abstract page: | 118 | Full-text PDF : | 62 | First page: | 1 |
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