Publikationsserver
Total anti-symmetrische Quasigruppen
Bei der Untersuchung von Prüfziffersystemen über Quasigruppen stößt man auf die so genannten total anti-symmetrischen Quasigruppen. Bislang war ihre Existenz für alle Ordnungen $4k+2\geq 10$ ungeklärt. Ecker und Poch vermuteten 1986, dass es keine total anti-symmetrischen Quasigruppen der Ordnung $4...
| मुख्य लेखक: | |
|---|---|
| अन्य लेखक: | |
| स्वरूप: | Dissertation |
| भाषा: | जर्मन |
| प्रकाशित: |
Philipps-Universität Marburg
2004
|
| विषय: | |
| ऑनलाइन पहुंच: | पीडीएफ पूर्ण पाठ |
| टैग: |
टैग जोड़ें
कोई टैग नहीं, इस रिकॉर्ड को टैग करने वाले पहले व्यक्ति बनें!
|
Totally anti-symmetric quasigroups are employed in check digit systems. Until today their existence for all orders $4k+2\geq 10$ was unsettled. Ecker and Poch conjectured in 1986 that there are no totally anti-symmetric quasigroups of order $4k+2$. We disprove this conjecture and develop constructions for totally anti-symmetric quasigroups of order $n$ for all $n\neq 2,6$. By a computer search we prove in addition that check digit systems over a 2-quasigroup of the order 10, just as check digit systems over groups of order 10, cannot detect all (jump) twin errors or jump transpositions. As a further result we show that the class of totally anti-symmetric quasigroups is no variety.