Excellent codes from modular curves
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Sparse polynomial approximation in finite fields
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Decoding Hermitian Codes with Sudan's Algorithm
AAECC-13 Proceedings of the 13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
On Fast Interpolation Method for Guruswami-Sudan List Decoding of One-Point Algebraic-Geometry Codes
AAECC-14 Proceedings of the 14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Ideal Error-Correcting Codes: Unifying Algebraic and Number-Theoretic Algorithms
AAECC-14 Proceedings of the 14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Constructions of Codes from Number Fields
AAECC-14 Proceedings of the 14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Efficient Traitor Tracing Algorithms Using List Decoding
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
List Decoding: Algorithms and Applications
TCS '00 Proceedings of the International Conference IFIP on Theoretical Computer Science, Exploring New Frontiers of Theoretical Informatics
On Representations of Algebraic-Geometric Codes for List Decoding
ESA '00 Proceedings of the 8th Annual European Symposium on Algorithms
Noisy Chinese remaindering in the Lee norm
Journal of Complexity - Special issue on coding and cryptography
A displacement approach to decoding algebraic codes
Contemporary mathematics
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
List decoding of Hermitian codes using Gröbner bases
Journal of Symbolic Computation
Designs, Codes and Cryptography
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
Algebraic soft-decision decoding of Hermitian codes
IEEE Transactions on Information Theory
Minimum distance decoding of general algebraic geometry codes via lists
IEEE Transactions on Information Theory
Improved decoding of interleaved AG codes
IMA'05 Proceedings of the 10th international conference on Cryptography and Coding
Bounds on collaborative decoding of interleaved Hermitian codes and virtual extension
Designs, Codes and Cryptography
| Hi-index | 754.96 |
We generalize Sudan's (see J. Compl., vol.13, p.180-93, 1997) results for Reed-Solomon codes to the class of algebraic-geometric codes, designing algorithms for list decoding of algebraic geometric codes which can decode beyond the conventional error-correction bound (d-1)/2, d being the minimum distance of the code. Our main algorithm is based on an interpolation scheme and factorization of polynomials over algebraic function fields. For the latter problem we design a polynomial-time algorithm and show that the resulting overall list-decoding algorithm runs in polynomial time under some mild conditions. Several examples are included