Towards the Best Choice of Quasigroups for Error Detection with an Error-Detecting Code

This paper refers to an error-detecting code that we previously defined and analyzed from several aspects. The goal of the paper is to answer whether the quasigroups of order 4 for which the code achieves largest probability of error detection also provide largest number of surely detected faulty bits (FBD). For this reason, we run simulations over the set of quasigroups of order 4 that we have previously determined as suitable for coding with the considered code. While theoretical analysis of the code concerns only the cases when for coding are used linear quasigroups, in this paper we obtained experimental results not only when linear, but also when nonlinear quasigroups are used for coding, too. Using this simulation, we give answer whether the quasigroups that provide maximal probability of error detection are overall best for coding with this code. Additionally, from the results from the simulations, we obtain some additional properties of the code.