A new procedure for decoding cyclic and BCH codes up to actual minimum distance
- 1 September 1994
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Information Theory
- Vol. 40 (5) , 1364-1374
- https://doi.org/10.1109/18.333854
Abstract
The paper presents a new procedure for decoding cyclic and BCH codes up to their actual minimum distance. It generalizes the Peterson decoding procedure and the procedure of Feng and Tzeng (1991) using nonrecurrent syndrome dependence relations. For a code with actual minimum distance d to correct up to t=[(d-1)/2] errors, the procedure requires a (2t+1)/spl times/(2t+1) syndrome matrix with known syndromes above the minor diagonal and unknown syndromes and their conjugates on the minor diagonal. In contrast to previous procedures, this procedure is primarily aimed at solving for the unknown syndromes instead of determining an error-locator polynomial. Decoding is then accomplished by determining the error vector as the inverse Fourier transform of the syndrome vector (S/sub 0/, S/sub 1/, S/sub n-1/). The authors show that with this procedure, all binary cyclic and BCH codes of lengthKeywords
This publication has 8 references indexed in Scilit:
- The algebraic decoding of the (41, 21, 9) quadratic residue codeIEEE Transactions on Information Theory, 1992
- Decoding cyclic and BCH codes up to actual minimum distance using nonrecurrent syndrome dependence relationsIEEE Transactions on Information Theory, 1991
- Algebraic decoding of the (32, 16, 8) quadratic residue codeIEEE Transactions on Information Theory, 1990
- Algebraic decoding beyond e/sub BCH/ of some binary cyclic codes, when e>e/sub BCH/IEEE Transactions on Information Theory, 1990
- Extension of the BCH decoding algorithm to decode binary cyclic codes up to their maximum error correction capacitiesIEEE Transactions on Information Theory, 1988
- Algebraic decoding of the (23,12,7) Golay code (Corresp.)IEEE Transactions on Information Theory, 1987
- On the minimum distance of cyclic codesIEEE Transactions on Information Theory, 1986
- Shift-register synthesis and BCH decodingIEEE Transactions on Information Theory, 1969