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IMCS/Publications/QRS/Issues/QRS v.10, n.1 (10), 2003/

Check character systems over quasigroups and loops

Authors: Beliavscaia Galina, Izbaş Vladimir, Şcerbacov Victor

Abstract

In this paper we survey the known results concerning check character (or digit) systems with one check character based on quasigroups (loops, groups). These are codes with one control symbol detecting errors of specific types. This survey includes the following sections: 1. Introduction. 2. Check character systems over groups. 3. Check character systems over quasigroups. 4. Check character systems over T-quasigroups. 5. Detection sets and detection rate. 6. Equivalence of check character systems. 7. Check character systems as n-ary operations.

Beliavscaia Galina,
Izbaş Vladimir,
Şcerbacov Victor Institute of Mathematics and Computer Science,
Academy of Sciences of Moldova,
str. Academiei 5,
MD-2028 Chisinau,
Moldova.
E-mail: (G.B.Beliavscaia)
E-mail: (V.I.Izbaş)
E-mail: (V.A.Şcerbacov)

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