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Decoding of the Five-Error-Correcting Binary Quadratic Residue Codes
American Journal of Mathematical and Computer Modelling
Volume 2, Issue 1, February 2017, Pages: 6-12
Received: Oct. 29, 2016; Accepted: Nov. 28, 2016; Published: Jan. 6, 2017
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Authors
Yani Zhang, School of Mathematics & Statistics, Southwest University, Chongqing, China
Xiaomin Bao, School of Mathematics & Statistics, Southwest University, Chongqing, China
Zhihua Yuan, School of Mathematics & Statistics, Southwest University, Chongqing, China
Xusheng Wu, School of Mathematics & Statistics, Southwest University, Chongqing, China
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Abstract
In this paper, a new efficient syndrome-weight decoding algorithm (NESWDA) is presented to decode up to five possible errors in a binary systematic (47, 24, 11) quadratic residue (QR) code. The main idea of NESWDA is based on the property cyclic codes together with the weight of syndrome difference. The advantage of the NESWDA decoding algorithm over the previous table look-up methods is that it has no need of a look-up table to store the syndromes and their corresponding error patterns in the memory. Moreover, it can be extended to decode all five-error-correcting binary QR codes.
Keywords
Cyclic Codes, Decoding, Quadratic Residue Code
To cite this article
Yani Zhang, Xiaomin Bao, Zhihua Yuan, Xusheng Wu, Decoding of the Five-Error-Correcting Binary Quadratic Residue Codes, American Journal of Mathematical and Computer Modelling. Vol. 2, No. 1, 2017, pp. 6-12. doi: 10.11648/j.ajmcm.20170201.12
Copyright
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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