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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 this paper, a simplified decoding algorithm of the (23, 12, 7) Golay code with error-correcting capacity less than or equal to 3 is proposed. The simulation result of the decoding algorithm is shown that all correctable error patterns are decoded successfully via the simplified decoding algorithm.
In this paper, a modified decoding method is proposed for the binary quadratic residue (QR) codes. The key ideal behind the proposed method is to apply the properties of remainder decoding and the modified Gao's algorithm. In the decoding method, the main features are efficient to compute syndromes and determine the error-locator polynomial. And the modified Gao's algorithm is also developed in our...
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 simple decoding scheme for the quadratic residue codes that utilize extended Euclidpsilas algorithm is proposed. This decoding method is based on the property of the syndrome polynomial to obtain the error-locator polynomial. Moreover, the simulation results for comparing the new decoding method with a proposed method are given.
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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