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<oai_dc:dc xmlns:dc='http://purl.org/dc/elements/1.1/' xmlns:oai_dc='http://www.openarchives.org/OAI/2.0/oai_dc/' xmlns:xsi='http://www.w3.org/2001/XMLSchema-instance' xsi:schemaLocation='http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd'>
<dc:creator>Ilievska, N.</dc:creator>
<dc:date>2014-12-24</dc:date>
<dc:description xml:lang='en'>In one previous paper, we proposed a new model of error-detecting codes base on  quasigroups  on  the   following  way.   Each   input   block   ai a2 . . . an   is  extended   to   a  blockl a1a2 . . . anb1b2 . . . bn  where  bi  = ai  * ari i  * ari 2    * ari k - I  '  i E  {1, 2, . . . , n},  * is  a  quasil group operation and r j  = { j,       d         .i ,,::; n   . We have already derived approximate formula! J   mo   n,   J > n for the probability  of undetected  errors when  quasigroups  of order  4 are used  for coding ancl k = 2. In this paper, we derive approximate formula for the probability  of  undetected  error when also quasigroups of order  4 are used for coding, but k = 3. We find the optimal blockl length such that the probability  of undetected  errors is smaller than some previously given valu r=:    and  give classification  of  quasigroups  of  order  4 according to goodness  for the  code when  k  = 3.I Also, we compare these two considered codes and conclude that the best  set of quasigroups forl coding for both codes contains only linear fractal  quasigroups  and  the  code with  k  = 3 give much smaller probability of undetected errors. At the end, we compare the code considered inl this paper with well-known  error-detecting codes:  CRC, Hamming and Reed-Muller.  </dc:description>
<dc:source>Quasigroups and Related Systems 32 (2) 223-246</dc:source>
<dc:title>Proving the probability of undetected errors for an error-detecting code based on quasigroups</dc:title>
<dc:type>info:eu-repo/semantics/article</dc:type>
</oai_dc:dc>