List decoding of Reed-Solomon codes from a Gröbner basis perspective
Journal of Symbolic Computation
A Syndrome Formulation of the Interpolation Step in the Guruswami-Sudan Algorithm
ICMCTA '08 Proceedings of the 2nd international Castle meeting on Coding Theory and Applications
Key equations for list decoding of Reed-Solomon codes and how to solve them
Journal of Symbolic Computation
Algebraic soft-decision decoding of Hermitian codes
IEEE Transactions on Information Theory
Efficient interpolation in the Guruswami-Sudan algorithm
IEEE Transactions on Information Theory
Efficiently decodable non-adaptive group testing
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
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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This paper generalizes the classical Knuth-Schoumlnhage algorithm computing the greatest common divisor (gcd) of two polynomials for solving arbitrary linear Diophantine systems over polynomials in time, quasi-linear in the maximal degree. As an application, the following weighted curve fitting problem is considered: given a set of points in the plane, find an algebraic curve (satisfying certain degree conditions) that goes through each point the prescribed number of times. The main motivation for this problem comes from coding theory, namely, it is ultimately related to the list decoding of Reed-Solomon codes. This paper presents a new fast algorithm for the weighted curve fitting problem, based on the explicit construction of a Groebner basis. This gives another fast algorithm for the soft decoding of Reed-Solomon codes different from the procedure proposed by Feng, which works in time (w/r) O(1)nlog2n, where r is the rate of the code, and w is the maximal weight assigned to a vertical line