Study on the algebraic decoding of the (89, 45, 17) quadratic residue code

A study on the weight-5 error patterns of the algebraic decoding of the (89, 45, 17) quadratic residue (QR) code with reducible generator polynomial, proposed by Truong et al. (2008), is presented. For the QR codes with irreducible generator polynomial, S 1 = 0 means that the received word has no er...

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Bibliographic Details
Published in:2012 2nd International Conference on Consumer Electronics, Communications and Networks pp. 2124 - 2127
Main Author: Hung-Peng Lee
Format: Conference Proceeding
Language:English
Published: IEEE 01.04.2012
Subjects:
algebraic decoding algorithm
Algorithm design and analysis
Decoding
Encoding
error pattern
Generators
Hamming distance
Polynomials
quadratic residue code
syndrome
Systematics
ISBN:9781457714146, 1457714140
Online Access:Get full text
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Summary:A study on the weight-5 error patterns of the algebraic decoding of the (89, 45, 17) quadratic residue (QR) code with reducible generator polynomial, proposed by Truong et al. (2008), is presented. For the QR codes with irreducible generator polynomial, S 1 = 0 means that the received word has no errors. For the (89, 45, 17) QR codes, some weight-5 error patterns will cause a zero value in syndrome S 1 . However, these weight-5 error patterns do not cause a decoding failure while using the inverse-free Berlekamp-Massey (IFBM) algorithm to determine the error-locator polynomial. An example shows the facts.
ISBN:9781457714146
1457714140
DOI:10.1109/CECNet.2012.6201692