Introduction to finite fields and their applications
Introduction to finite fields and their applications
Decoding Affine Variety Codes Using Gröbner Bases
Designs, Codes and Cryptography
Order Functions and Evaluation Codes
AAECC-12 Proceedings of the 12th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Improved geometric Goppa codes. I. Basic theory
IEEE Transactions on Information Theory - Part 1
The second and third generalized Hamming weights of Hermitian 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 codes from norm-trace curves
Finite Fields and Their Applications
On the Structure of Order Domains
Finite Fields and Their Applications
Evaluation codes from order domain theory
Finite Fields and Their Applications
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Constructing new codes from existing ones by puncturing is in this paper viewed in the context of order domains R where puncturing can be seen as redefinition of the evaluation map @f:R-F"q^n. The order domains considered here are of the form R=F[x"1,x"2,...,x"m]/I where redefining @f can be done by adding one or more polynomials to the basis of the defining ideal I to form a new ideal J in such a way that the number of points in the variety V(I) is reduced by t to form V(J) and puncturing in t coordinates is achieved. An explicit construction of such polynomials is given in the case of codes defined by Norm-Trace curves and examples are given of both evaluation codes and dual codes. Finally, it is demonstrated that the improvement in minimum distance can be significant when compared to the lower bound obtained by ordinary puncturing.