On check character systems over quasigroups and loops

• Date: 2018
• 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
• Journal Title: Algebra and Discrete Mathematics

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^{...