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
ISSN
15579654
Abstract
Summary: ``The techniques needed to decode the (47, 24, 11) quadraticresidue (QR) code differ from the schemes developed for cyclic codesin [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, IEEETrans. Inform. Theory {\bf 40} (1994), no. 5, 1364--1374; Zbl0813.94015; I. M. Duursma and R. Kötter, IEEE Trans. Inform. Theory {\bf 40}(1994), no.~4, 1108--1121; MR1301421 (95h:94039)]. By finding certain nonlinearrelations between the known and unknown syndromes for this specialcode, two methods are developed to decode up to the true minimumdistance of the (47, 24, 11) QR code. These algorithms can be utilizedto decode effectively the $\frac 12$-rate (48, 24, 12) QR code forcorrecting five errors and detecting six errors.''