Decoding of Reed Solomon codes beyond the error-correction bound
Journal of Complexity
A displacement approach to efficient decoding of algebraic-geometric codes
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Modern Computer Algebra
List decoding of Reed-Solomon codes from a Gröbner basis perspective
Journal of Symbolic Computation
Improved decoding of Reed-Solomon and algebraic-geometry codes
IEEE Transactions on Information Theory
Efficient decoding of Reed-Solomon codes beyond half the minimum distance
IEEE Transactions on Information Theory
Linear diophantine equations over polynomials and soft decoding of Reed-Solomon codes
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
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
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A Reed-Solomon code of length n can be list decoded using the well-known Guruswami-Sudan algorithm. By a result of Alekhnovich (2005) the interpolation part in this algorithm can be done in complexity O(s^4l^4nlog^2nloglogn), where l denotes the designed list size and s the multiplicity parameter. The parameters l and s are sometimes considered to be constants in the complexity analysis, but for high rate Reed-Solomon codes, their values can be very large. In this paper we will combine ideas from Alekhnovich (2005) and the concept of key equations to get an algorithm that has complexity O(sl^4nlog^2nloglogn). This compares favorably to the complexities of other known interpolation algorithms.