Weierstrass Pairs and Minimum Distance of Goppa Codes
Designs, Codes and Cryptography
On Goppa Codes and Weierstrass Gaps at Several Points
Designs, Codes and Cryptography
Journal of Pure And Applied Algebra
Improvements on parameters of one-point AG codes from Hermitian curves
IEEE Transactions on Information Theory
Codes from the Suzuki function field
IEEE Transactions on Information Theory
On Weierstrass Semigroups of Some Triples on Norm-Trace Curves
IWCC '09 Proceedings of the 2nd International Workshop on Coding and Cryptology
Key Predistribution Schemes and One-Time Broadcast Encryption Schemes from Algebraic Geometry Codes
Cryptography and Coding '09 Proceedings of the 12th IMA International Conference on Cryptography and Coding
Codes from Riemann-Roch spaces for y2 = xp - x over GF(p)
International Journal of Information and Coding Theory
One-point AG codes on the GK maximal curves
IEEE Transactions on Information Theory
Minimum distance decoding of general algebraic geometry codes via lists
IEEE Transactions on Information Theory
| Hi-index | 0.12 |
We consider the quotient of the Hermitian curve defined by the equation yq + y = xm over $${\mathbb F}_{q^2}$$ where m 2 is a divisor of q+1. For 2驴 r 驴 q+1, we determine the Weierstrass semigroup of any r-tuple of $${\mathbb F}_{q^2}$$ -rational points $$(P_\infty, P_{0b_2},\ldots,P_{0b_r})$$ on this curve. Using these semigroups, we construct algebraic geometry codes with minimum distance exceeding the designed distance. In addition, we prove that there are r-point codes, that is codes of the form $$C_\Omega(D, \alpha_1P_\infty, \alpha_2P_{0b_2},+\cdots+ \alpha_rP_{0b_r})$$ where r 驴 2, with better parameters than any comparable one-point code on the same curve. Some of these codes have better parameters than comparable one-point Hermitian codes over the same field. All of our results apply to the Hermitian curve itself which is obtained by taking m=q +1 in the above equation