Decoding Affine Variety Codes Using Gröbner Bases
Designs, Codes and Cryptography
The minimum distance of some binary codes via the Newton's identities
EUROCODE '90 Proceedings of the International Symposium on Coding Theory and Applications
A Singular Introduction to Commutative Algebra
A Singular Introduction to Commutative Algebra
Efficient algorithms for solving overdefined systems of multivariate polynomial equations
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
A general framework for applying FGLM techniques to linear codes
AAECC'06 Proceedings of the 16th international conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
The hardness of decoding linear codes with preprocessing
IEEE Transactions on Information Theory
Shift-register synthesis and BCH decoding
IEEE Transactions on Information Theory
Decoding beyond the BCH bound (Corresp.)
IEEE Transactions on Information Theory
Decoding beyond the BCH bound using multiple sets of syndrome sequences (Corresp.)
IEEE Transactions on Information Theory
Studying the locator polynomials of minimum weight codewords of BCH codes
IEEE Transactions on Information Theory
Decoding the ternary Golay code
IEEE Transactions on Information Theory
Use of Grobner bases to decode binary cyclic codes up to the true minimum distance
IEEE Transactions on Information Theory
General principles for the algebraic decoding of cyclic codes
IEEE Transactions on Information Theory
| Hi-index | 0.00 |
The problem of bounded distance decoding of arbitrary linear codes using Grobner bases is addressed. A new method is proposed, which is based on reducing an initial decoding problem to solving a certain system of polynomial equations over a finite field. The peculiarity of this system is that, when we want to decode up to half the minimum distance, it has a unique solution even over the algebraic closure of the considered finite field, although field equations are not added. The equations in the system have degree at most 2. As our experiments suggest, our method is much faster than the one of Fitzgerald-Lax. It is also shown via experiments that the proposed approach in some range of parameters is superior to the generic syndrome decoding.