Finite field for scientists and engineers
Finite field for scientists and engineers
A course in number theory and cryptography
A course in number theory and cryptography
McEliece Public Key Cryptosystems Using Algebraic-Geometric Codes
Designs, Codes and Cryptography
Decoding Affine Variety Codes Using Gröbner Bases
Designs, Codes and Cryptography
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
A Course in Error-Correcting Codes (EMS Textbooks in Mathematics)
A Course in Error-Correcting Codes (EMS Textbooks in Mathematics)
Complexity Reduction of Constant Matrix Computations over the Binary Field
WAIFI '07 Proceedings of the 1st international workshop on Arithmetic of Finite Fields
Grbner Bases, Coding, and Cryptography
Grbner Bases, Coding, and Cryptography
Footprints or generalized Bezout's theorem
IEEE Transactions on Information Theory
On the dimension of subfield subcodes
IEEE Transactions on Information Theory
On subfield subcodes of modified Reed-Solomon codes (Corresp.)
IEEE Transactions on Information Theory
Fast decoding of codes from algebraic plane curves
IEEE Transactions on Information Theory
A note on Hermitian codes over GF(q2)
IEEE Transactions on Information Theory - Part 1
On codes from norm-trace curves
Finite Fields and Their Applications
| Hi-index | 0.00 |
We present a fast algorithm using Gröbner basis to compute the dimensions of subfield subcodes of Hermitian codes. With these algorithms we are able to compute the exact values of the dimension of all subfield subcodes up to q ≤ 32 and length up to 215. We show that some of the subfield subcodes of Hermitian codes are at least as good as the previously known codes, and we show the existence of good long codes.