VLSI Architectures for Computing Multiplications and Inverses in GF(2m)
IEEE Transactions on Computers
Algebraic decoding of the (23,12,7) Golay code
IEEE Transactions on Information Theory
Error control systems for digital communication and storage
Error control systems for digital communication and storage
Error-Control Coding for Data Networks
Error-Control Coding for Data Networks
A Lookup Table Decoding of systematic (47,24,11) quadratic residue code
Information Sciences: an International Journal
Algebraic decoding of the (41, 21, 9) Quadratic Residue code
Information Sciences: an International Journal
Decoding golay code by direct solution of the error locator polynomial
ICACT'09 Proceedings of the 11th international conference on Advanced Communication Technology - Volume 2
Grbner Bases, Coding, and Cryptography
Grbner Bases, Coding, and Cryptography
High speed decoding of the binary (47,24,11) quadratic residue code
Information Sciences: an International Journal
Algebraic decoding of the (32, 16, 8) quadratic residue code
IEEE Transactions on Information Theory
Use of Grobner bases to decode binary cyclic codes up to the true minimum distance
IEEE Transactions on Information Theory
Efficient decoding of the (23, 12, 7) Golay code up to five errors
Information Sciences: an International Journal
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An improved syndrome shift-register decoding algorithm, called the syndrome-weight decoding algorithm, is proposed for decoding three possible errors and detecting four errors in the (24,12,8) Golay code. This method can also be extended to decode two other short codes, such as the (15,5,7) cyclic code and the (31,16,7) quadratic residue (QR) code. The proposed decoding algorithm makes use of the properties of cyclic codes, the weight of syndrome, and the syndrome decoder with a reduced-size lookup table (RSLT) in order to reduce the number of syndromes and their corresponding coset leaders. This approach results in a significant reduction in the memory requirement for the lookup table, thereby yielding a faster decoding algorithm. Simulation results show that the decoding speed of the proposed algorithm is approximately 3.6 times faster than that of the algebraic decoding algorithm.