We will define two models of error-detecting codes based on quasigroups of arbitrary order. For some special cases of these two models we provide experimental results for the probability of undetected errors if a give...
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ISBN:
(纸本)9781479961917
We will define two models of error-detecting codes based on quasigroups of arbitrary order. For some special cases of these two models we provide experimental results for the probability of undetected errors if a given quasigroup of order 4 is used for coding. At the end, we will compare the considered special cases.
In this paper we consider an error-detecting code based on linear quasigroups. We give a proof that the code is linear. Also, we obtain the generator and the parity-check matrices of the code, from where we obtain the...
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ISBN:
(数字)9783319675978
ISBN:
(纸本)9783319675978;9783319675961
In this paper we consider an error-detecting code based on linear quasigroups. We give a proof that the code is linear. Also, we obtain the generator and the parity-check matrices of the code, from where we obtain the Hamming distance of the code when a linear quasigroup of order 4 from the best class of quasigroups of order 4 for coding, i.e., the class of quasigroups of order 4 that gives smallest probability of undetected errors is used for coding. With this we determine the number of errors that the code will detect for sure.
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