Designs, Codes and Cryptography
A class of I.P.P. codes with efficient identification
Journal of Complexity - Special issue on coding and cryptography
On Hash Functions and List Decoding with Side Information
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
List decoding codes on Garcia-Stictenoth tower using Gröbner basis
Journal of Symbolic Computation
A polynomial-time construction of self-orthogonal codes and applications to quantum error correction
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
On the computation of non-uniform input for list decoding on Bezerra-Garcia tower
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
On constructing AG codes without basis functions for riemann-roch spaces
AAECC'06 Proceedings of the 16th international conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Algebraic geometric secret sharing schemes and secure multi-party computations over small fields
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
Folded codes from function field towers and improved optimal rate list decoding
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
On rational embeddings of curves in the second Garcia--Stichtenoth tower
Finite Fields and Their Applications
Finite Fields and Their Applications
Integral closures and weight functions over finite fields
Finite Fields and Their Applications
A new method for constructing small-bias spaces from hermitian codes
WAIFI'12 Proceedings of the 4th international conference on Arithmetic of Finite Fields
| Hi-index | 754.84 |
Since the proof in 1982, by Tsfasman Vladut and Zink of the existence of algebraic-geometric (AG) codes with asymptotic performance exceeding the Gilbert-Varshamov (G-V) bound, one of the challenges in coding theory has been to provide explicit constructions for these codes. In a major step forward during 1995-1996, Garcia and Stichtenoth (GS) provided an explicit description of algebraic curves, such that AG codes constructed on them would have a performance better than the G-V bound. We present the first low-complexity algorithm for obtaining the generator matrix for AG codes on the curves of GS. The symbol alphabet of the AG code is the finite field of q2, q2⩾49, elements. The complexity of the algorithm, as measured in terms of multiplications and divisions over the finite field GF(q2), is upper-bounded by [Nlogq(N)]3 where N is the length of the code. An example of code construction using the above algorithm is presented. By concatenating the AG code with short binary block codes, it is possible to obtain binary codes with asymptotic performance close to the G-V bound. Some examples of such concatenation are included