Use characteristic sets to decode cyclic codes up to actual minimum distance
FFA '95 Proceedings of the third international conference on Finite fields and applications
Introduction to Coding Theory and Algebraic Geometry
Introduction to Coding Theory and Algebraic Geometry
The Construction of Multivariate Polynomials with Preassigned Zeros
EUROCAM '82 Proceedings of the European Computer Algebra Conference on Computer Algebra
Improved geometric Goppa codes. I. Basic theory
IEEE Transactions on Information Theory - Part 1
IEEE Transactions on Information Theory - Part 1
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
Bounded distance decoding of linear error-correcting codes with Gröbner bases
Journal of Symbolic Computation
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
A new method for constructing small-bias spaces from hermitian codes
WAIFI'12 Proceedings of the 4th international conference on Arithmetic of Finite Fields
On the subfield subcodes of Hermitian codes
Designs, Codes and Cryptography
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We define a class of codes that we call affine varietycodes. These codes are obtained by evaluating functions in thecoordinate ring of an affine variety on all the F_q-rationalpoints of the variety. We show that one can, at least in theory,decode these codes up to half the true minimum distance by usingthe theory of Gröbner bases. We extend results of A. B.Cooper and of X. Chen, I. S. Reed, T. Helleseth, and T. K. Truong.