Introduction to finite fields and their applications
Introduction to finite fields and their applications
Fast Probabilistic Algorithms for Verification of Polynomial Identities
Journal of the ACM (JACM)
AAECC-14 Proceedings of the 14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Probabilistic algorithms for sparse polynomials
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
Toric Codes over Finite Fields
Applicable Algebra in Engineering, Communication and Computing
Toric Surface Codes and Minkowski Sums
SIAM Journal on Discrete Mathematics
On the structure of generalized toric codes
Journal of Symbolic Computation
Extensions to the Method of Multiplicities, with Applications to Kakeya Sets and Mergers
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
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
Improved geometric Goppa codes. I. Basic theory
IEEE Transactions on Information Theory - Part 1
Improved decoding of Reed-Solomon and algebraic-geometry codes
IEEE Transactions on Information Theory
New generalizations of the Reed-Muller codes--I: Primitive codes
IEEE Transactions on Information Theory
Polynomial weights and code constructions
IEEE Transactions on Information Theory
List decoding of q-ary Reed-Muller codes
IEEE Transactions on Information Theory
Weighted Reed-Muller codes and algebraic-geometric codes
IEEE Transactions on Information Theory
A simple approach for construction of algebraic-geometric codes from affine plane curves
IEEE Transactions on Information Theory
On the parameters of r-dimensional toric codes
Finite Fields and Their Applications
Evaluation codes from order domain theory
Finite Fields and Their Applications
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We consider weighted Reed---Muller codes over point ensemble S 1 脳 · · · 脳 S m where S i needs not be of the same size as S j . For m = 2 we determine optimal weights and analyze in detail what is the impact of the ratio |S 1|/|S 2| on the minimum distance. In conclusion the weighted Reed---Muller code construction is much better than its reputation. For a class of affine variety codes that contains the weighted Reed---Muller codes we then present two list decoding algorithms. With a small modification one of these algorithms is able to correct up to 31 errors of the [49,11,28] Joyner code.