On check character systems over quasigroups and loops

• Published in: Algebra and Discrete Mathematics
• Date: 2003
• Main Author: Belyavskaya, G.B.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2003
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/155694
• 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.

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...