Belyavskaya, G.; Diordiev, A. On some quasi-identities in finite quasigroups. (English) Zbl 1107.20058 Bul. Acad. Ştiinţe Repub. Mold., Mat. 2005, No. 3(49), 19-32 (2005). Summary: We consider some quasi-identities in quasigroups, in particular, quasi-identities connected with parastrophic orthogonality of a quasigroup. We also investigate some quasi-identities in quasigroups (in loops) with one parameter \(\delta\) (\(\delta\)-quasi-identities) which arose in the study of detecting coding systems such as check character systems [by G. B. Belyavskaya, V. I. Izbash and G. L. Mullen, Des. Codes Cryptography 37, No. 2, 215-227 (2005; Zbl 1102.94031)], establish equivalence of such quasi-identities, connection of some of them with orthogonality of quasigroups and give a number of examples of finite quasigroups with such \(\delta\)-quasi-identities. Cited in 2 Documents MSC: 20N05 Loops, quasigroups 94B60 Other types of codes Keywords:finite quasigroups; loops; automorphisms; quasi-identities; parastrophic orthogonalities Citations:Zbl 1102.94031 PDFBibTeX XMLCite \textit{G. Belyavskaya} and \textit{A. Diordiev}, Bul. Acad. Științe Repub. Mold., Mat. 2005, No. 3(49), 19--32 (2005; Zbl 1107.20058)