Decoding Affine Variety Codes Using Gröbner Bases
Designs, Codes and Cryptography
AAECC-14 Proceedings of the 14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Redundancies of correction capability optimized Reed-Muller codes
Discrete Applied Mathematics
The Order Bound for Toric Codes
AAECC-18 '09 Proceedings of the 18th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
On numerical semigroups and the redundancy of improved codes correcting generic errors
Designs, Codes and Cryptography
On Linear Codes from Maximal Curves
Cryptography and Coding '09 Proceedings of the 12th IMA International Conference on Cryptography and Coding
Improvements to evaluation codes and new characterizations of Arf semigroups
AAECC'03 Proceedings of the 15th international conference on Applied algebra, algebraic algorithms and error-correcting codes
Extended norm-trace codes with optimized correction capability
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
On the feng-rao bound for generalized hamming weights
AAECC'06 Proceedings of the 16th international conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Evaluation codes from order domain theory
Finite Fields and Their Applications
On puncturing of codes from Norm--Trace curves
Finite Fields and Their Applications
An improvement of the Feng--Rao bound on minimum distance
Finite Fields and Their Applications
On codes from norm-trace curves
Finite Fields and Their Applications
Weighted Reed---Muller codes revisited
Designs, Codes and Cryptography
Evaluation codes defined by finite families of plane valuations at infinity
Designs, Codes and Cryptography
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In this paper, we present a construction of improved geometric Goppa codes which, for the case of r<2g, are often more efficient than the current geometric Goppa codes derived from some varieties, which include algebraic curves, hyperplanes, surfaces, and other varieties. For the special case of a plane in a three-dimensional projective space, the improved geometric Goppa codes are reduced to linear multilevel codes. For these improved geometric Goppa codes, a designed minimum distance can be easily determined and a decoding procedure which corrects up to half the designed minimum distance is also given