Gro¨bner bases: a computational approach to commutative algebra
Gro¨bner bases: a computational approach to commutative algebra
Interpolation in list decoding of Reed-Solomon codes
Problems of Information Transmission
List decoding of Reed-Solomon codes from a Gröbner basis perspective
Journal of Symbolic Computation
Fast generalized minimum-distance decoding of algebraic-geometry and Reed-Solomon codes
IEEE Transactions on Information Theory
Improved decoding of Reed-Solomon and algebraic-geometry codes
IEEE Transactions on Information Theory
A simple algorithm for decoding Reed-Solomon codes and its relation to the Welch-Berlekamp algorithm
IEEE Transactions on Information Theory
Linear diophantine equations over polynomials and soft decoding of Reed-Solomon codes
IEEE Transactions on Information Theory
New List Decoding Algorithms for Reed–Solomon and BCH Codes
IEEE Transactions on Information Theory
Simplified high-speed high-distance list decoding for alternant codes
PQCrypto'11 Proceedings of the 4th international conference on Post-Quantum Cryptography
| Hi-index | 754.84 |
A novel algorithm is proposed for the interpolation step of the Guruswami-Sudan list decoding algorithm. The proposed method is based on the binary exponentiation algorithm, and can be considered as an extension of the Lee-O'Sullivan method. The algorithm is shown to achieve both asymptotical and practical performance gain compared to the case of iterative interpolation algorithm. Further complexity reduction is achieved by employing the reencoding transformation. The key contribution of the paper, which enables the complexity reduction, is a novel randomized ideal multiplication algorithm.