학술논문
Decoding the $(47,24,11)$ quadratic residue code.
Document Type
Journal
Author
He, Ruhua (1-SCA-D) AMS Author Profile; Reed, Irving S. (RC-ISU-CEI) AMS Author Profile; Truong, Trieu-Kien (1-BDCM) AMS Author Profile; Chen, Xuemin AMS Author Profile
Source
Subject
94 Information and communication, circuits -- 94B Theory of error-correcting codes and error-detecting codes
94B27Geometric methods
94B27
Language
English
Abstract
Summary: ``The techniques needed to decode the (47, 24, 11) quadratic residue (QR) code differ from the schemes developed for cyclic codes in [I. S. Reed\ et al., IEEE Trans. Inform. Theory {\bf 38} (1992), no.~3, 974--986; MR1162824 (93h:94031); G. L. Feng and K. K. Tzeng, IEEE Trans. Inform. Theory {\bf 40} (1994), no. 5, 1364--1374; Zbl 0813.94015; I. M. Duursma\ and R. Kötter, IEEE Trans. Inform. Theory {\bf 40} (1994), no.~4, 1108--1121; MR1301421 (95h:94039)]. By finding certain nonlinear relations between the known and unknown syndromes for this special code, two methods are developed to decode up to the true minimum distance of the (47, 24, 11) QR code. These algorithms can be utilized to decode effectively the $\frac 12$-rate (48, 24, 12) QR code for correcting five errors and detecting six errors.''