List-decoding reed-muller codes over small fields
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
An improved list decoding algorithm for the second order Reed---Muller codes and its applications
Designs, Codes and Cryptography
List decoding tensor products and interleaved codes
Proceedings of the forty-first annual ACM symposium on Theory of computing
Generalized Sudan's list decoding for order domain codes
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
List decoding of generalized reed-solomon codes by using a modified extended key equation algorithm
EURASIP Journal on Wireless Communications and Networking
List Decoding Tensor Products and Interleaved Codes
SIAM Journal on Computing
Weighted Reed---Muller codes revisited
Designs, Codes and Cryptography
| Hi-index | 754.84 |
The q-ary Reed-Muller (RM) codes RMq(u,m) of length n=qm are a generalization of Reed-Solomon (RS) codes, which use polynomials in m variables to encode messages through functional encoding. Using an idea of reducing the multivariate case to the univariate case, randomized list-decoding algorithms for RM codes were given in and . The algorithm in Sudan et al. (1999) is an improvement of the algorithm in , it is applicable to codes RMq(u,m) with uqm. Then, using the list- decoding algorithm in Guruswami and Sudan (1999) for RS codes over Fqm, we present a list-decoding algorithm for q-ary RM codes. This algorithm is applicable to codes of any rates, and achieves an error-correction bound n(1-√(n-d)/n). The algorithm achieves a better error-correction bound than the algorithm in , since when u is small. The implementation of the algorithm requires O(n) field operations in Fq and O(n3) field operations in Fqm under some assumption.