Contribution to the Quasigroup Based Error-Detecting Code

• Published in: 2023 3rd International Conference on Electrical, Computer, Communications and Mechatronics Engineering (ICECCME) pp. 1 - 6
• Main Author: Ilievska, Natasha
• Format: Conference Proceeding
• Language: English
• Published: IEEE 19.07.2023
• Subjects: Codes; Encoding; error-detecting code; Hamming distance; Linear codes; linear quasi-group; Mechatronics; number of surely detected errors; quasigroup
• DOI: 10.1109/ICECCME57830.2023.10253159

In the last years we have developed few error-detecting codes based on quasigroups. One of them is the code which is a subject of this paper. The previous analyses of the code shows that the code has very high probability of detecting transmission errors. We have previously identified so-called best class of quasigroups of order 4, with the highest probability of detecting errors when the coding process is performed with a quasigroups of order 4. But, there is one more class of quasigroups of order 4, second-best class, whose quasigroups give approximately equal probability of undetected errors as the quasigroups from the best one. Therefore, we proceeded with the examination of the code when it uses quasigroups from this second-best class of quasigroups of order 4. In this paper we will analytically obtain the second important parameter of every error-detecting code, i.e. the number of errors that the code surely detects when for coding it uses a quasigroup from this second-best class of quasigroups of order 4. At the end we will conclude whether the quasigroups from these top two classes have overall equal ability to detect errors with this code.