Weierstrass Semigroups and Codes from a Quotient of the Hermitian Curve
Designs, Codes and Cryptography
Algebraic Geometry Codes from Castle Curves
ICMCTA '08 Proceedings of the 2nd international Castle meeting on Coding Theory and Applications
Two-Point Codes on Norm-Trace Curves
ICMCTA '08 Proceedings of the 2nd international Castle meeting on Coding Theory and Applications
An Extension of the Order Bound for AG Codes
AAECC-18 '09 Proceedings of the 18th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
On Weierstrass Semigroups of Some Triples on Norm-Trace Curves
IWCC '09 Proceedings of the 2nd International Workshop on Coding and Cryptology
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
The order bound for general algebraic geometric codes
Finite Fields and Their Applications
| Hi-index | 754.96 |
We construct algebraic geometry (AG) codes from the function field F(22n+1)(x,y)/F(22n+1) defined by y(22n+1)-y=(x(22n+)-x) where n is a positive integer. These codes are supported by two places, and many have parameters that are better than those of any comparable code supported by one place of the same function field. To define such codes, we determine and exploit the structure of the Weierstrass gap set of an arbitrary pair of rational places of F(22n+1)(x,y)/F(22n+1). Moreover, we find some codes over F8 with parameters that are better than any known code.