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Check character systems over quasigroups and loops
Authors: Beliavscaia Galina, Izbaş Vladimir, Şcerbacov Victor
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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)
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)
Fulltext
– 0.34 Mb
Contents
- Check character systems over quasigroups and loops
- Quasigroups constructed from cycle systems
- Octonions, simple Moufang loops and triality
- See Otter digging for algebraic pearls
- Quasigroup permutation representations
