NASA Logo

NTRS

NTRS - NASA Technical Reports Server

Back to Results
The algebraic decoding of the (41, 21, 9) quadratic residue codeA new algebraic approach for decoding the quadratic residue (QR) codes, in particular the (41, 21, 9) QR code is presented. The key ideas behind this decoding technique are a systematic application of the Sylvester resultant method to the Newton identities associated with the code syndromes to find the error-locator polynomial, and next a method for determining error locations by solving certain quadratic, cubic and quartic equations over GF(2 exp m) in a new way which uses Zech's logarithms for the arithmetic. The algorithms developed here are suitable for implementation in a programmable microprocessor or special-purpose VLSI chip. It is expected that the algebraic methods developed here can apply generally to other codes such as the BCH and Reed-Solomon codes.
Document ID
19920063395
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
External Source(s)
Authors
Reed, Irving S.
(Southern California, University Los Angeles, CA, United States)
Truong, T. K.
(JPL Pasadena, CA, United States)
Chen, Xuemin
(Jet Propulsion Lab., California Inst. of Tech. Pasadena, CA, United States)
Yin, Xiaowei
(Southern California, University Los Angeles, CA, United States)
Date Acquired
August 15, 2013
Publication Date
May 1, 1992
Publication Information
Publication: IEEE Transactions on Information Theory
Volume: 38
Issue: 3 Ma
ISSN: 0018-9448
Subject Category
Cybernetics
Accession Number
92A46019
Funding Number(s)
CONTRACT_GRANT: NSF NCR-90-16340
CONTRACT_GRANT: NSF NCR-89-20060
Distribution Limits
Public
Copyright
Other

Available Downloads

There are no available downloads for this record.
No Preview Available