Towards an Error-Detecting Code

In this paper we consider an error-detecting code that we have previously defined using quasigroups. The code is defined in the following way: Each input block a(0)a(1)... a(n-1) of symbols from the quasigroup used for coding is extended into block a(0)a(1)... a(n-1)d(0)d(1)... d(n-1), where the redundant symbols di, i is an element of {0, 1,..., n - 1}, are calculated using the quasigroup operation *, i.e., d(i) = a(i) *a(i+1) (mod n). In our previous work we classified the quasigroups of order 4 according to their probability of undetected errors. Since in our previous work we showed that the quasigroups in the first two classes give almost equal probabilities of undetected errors, now we will compare the quasigroups from these two classes according to the number of errors that the code surely detects when they are used for coding. In order to do this, first using simultions we will obtain the number of errors that the code surely detects when for coding is used a quasigroup from the second best class of quasigroups of order 4 for coding. We will show that from the aspect of the number of errors that the code surely detects, these quasigroups are equally good for coding as the quasigroups from the best class of quasigroups when the length of the input blocks is at least three characters from the quasigroup of order 4.