Algebraic-Geometric Codes
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
List decoding of algebraic-geometric codes
IEEE Transactions on Information Theory
Improved decoding of Reed-Solomon and algebraic-geometry codes
IEEE Transactions on Information Theory
On Towers and Composita of Towers of Function Fields over Finite Fields
Finite Fields and Their Applications
Improvements on parameters of algebraic-geometry codes from Hermitian curves
IEEE Transactions on Information Theory
Nonlinear codes from points of bounded height
Finite Fields and Their Applications
Further improvements on asymptotic bounds for codes using distinguished divisors
Finite Fields and Their Applications
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We introduce a new construction of error-correcting codes from algebraic curves over finite fields. Modular curves of genus g\ra\infty over a field of size q_0^2 yield nonlinear codes more efficient than the linear Goppa codes obtained from the same curves. These new codes now have the highest asymptotic transmission rates known for certain ranges of alphabet size and error rate. Both the theory and possible practical use of these new record codes require the development of new tools. On the theoretical side, establishing the transmission rate depends on an error estimate for a theorem of Schanuel applied to the function field of an asymptotically optimal curve. On the computational side, actual use of the codes will hinge on the solution of new problems in the computational algebraic geometry of curves.