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^{...
Gespeichert in:
| Datum: | 2018 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2018
|
| Schlagworte: | |
| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/955 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| Zusammenfassung: | 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. |
|---|