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An algebraic decoding of the (89, 45, 17) quadratic residue code suggested by Truong et al. (2008) has been designed that uses the inverse-free Berlekamp-Massey (BM) algorithm to determine the error-locator polynomial and applies a verification method to check whether the error pattern obtained by decoding algorithm is correct or not. In this paper, based on the ideas of the algorithm mentioned above,...
Binary quadratic residue (QR) codes, which have code rates greater than or equal to 1/2 and generally have large minimum distances, are among the best known codes. This paper considers a modified algebraic decoding algorithm for the (89,45,17) binary QR code that utilizes the Berlekamp-Massey algorithm. It identifies the primary unknown syndromes and provides methods to determine these on a case-by-case...
In order to use Berlekamp-Massey algorithm to decode the (89, 45, 17) binary quadratic residue code, one needs to determine two primary unknown syndromes. In this paper, the authors give some syndrome matrices, so as to calculate one primary unknown syndrome efficiently. This results in a reduction of decoding complexity in terms of CPU time by 35% at least versus the decoder proposed by Truong et...
This paper is to develop a modified algorithm for decoding the (48, 24, 12) binary quadratic residue code up to six errors. The technique in this paper uses the algebraic decoding algorithm for the (47, 24, 11) quadratic residue code offered by Truong et al. to correct up to five errors. Then, the technique of detecting a six-error is utilized. Finally, the reliability-search algorithm, proposed by...
In this paper, a classical decoder for the (89, 45, 17) binary quadratic residue code, the last one not decoded yet of length less than 100, is proposed. It was also verified for all error patterns within the error-correcting capacity of the code without checking all error patterns by computer simulations.
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