Using classes of equivalence in the detecting and correcting errors in the wordcode

Jusufi, Azir and Beqiri, Xhevair and Imeri-Jusufi, Bukurie (2018) Using classes of equivalence in the detecting and correcting errors in the wordcode. Journal of Natural Sciences and Mathematics of UT, 3 (5-6). pp. 152-156. ISSN 2671-3039

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Abstract

Developments in recent decades of the sector in digital communication have created a close relationship between mathematics and computer engineering. An important class of codes are linear codes in the vector space V (n, q) , where GF (q), is a finite field of order q. Let C be a linear [n, k] code. A generator matrix of C is a k × n matrix such that the rows are basis vectors of C [n, k]. If we specify V(n,q) as a vector space on then the linear binary code C[n,k] is nothing else, but a subspace of the vector space V(n,q). When transferring the wordcodes through different types of obstacle channels, errors may occur, which we need to detect and correct. With classes a+C, where a is a vector from V(n, q), we construct the standard group, which we will use to detect and correct the errors in the wordcode. If the word code c is sent, but the received vector is r, we define the error vector e = r − c. The error vector which will be corrected are precisely the coset leaders, irrespective of which wordcode is transmitted. By choosing a minimum weight vector in each coset as coset leader, we ensure that standard array decoding is a nearest neighbour decoding scheme.

Item Type:	Article
Subjects:	Q Science > Q Science (General)
Divisions:	Faculty of Engineering, Science and Mathematics > School of Mathematics
Depositing User:	Unnamed user with email zshi@unite.edu.mk
Date Deposited:	05 Jun 2019 08:34
Last Modified:	05 Jun 2019 08:34
URI:	http://eprints.unite.edu.mk/id/eprint/155

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