Isomorphism Classes of Hyperelliptic Curves of Genus 2 over Fq
ACISP '02 Proceedings of the 7th Australian Conference on Information Security and Privacy
Speeding up the Arithmetic on Koblitz Curves of Genus Two
SAC '00 Proceedings of the 7th Annual International Workshop on Selected Areas in Cryptography
Speeding up the Scalar Multiplication in the Jacobians of Hyperelliptic Curves Using Frobenius Map
INDOCRYPT '02 Proceedings of the Third International Conference on Cryptology: Progress in Cryptology
Supersingular Curves in Cryptography
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Efficient Traitor Tracing Algorithms Using List Decoding
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
An Algorithm for Computing Weierstrass Points
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
New Optimal Tame Towers of Function Fields over Small Finite Fields
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Improvements on Generalized Hamming Weights of Some Trace Codes
Designs, Codes and Cryptography
Ate Pairing on Hyperelliptic Curves
EUROCRYPT '07 Proceedings of the 26th annual international conference on Advances in Cryptology
A Syndrome Formulation of the Interpolation Step in the Guruswami-Sudan Algorithm
ICMCTA '08 Proceedings of the 2nd international Castle meeting on Coding Theory and Applications
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
On Hash Functions and List Decoding with Side Information
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Journal of Complexity
On improved asymptotic bounds for codes from global function fields
Designs, Codes and Cryptography
On algebras admitting a complete set of near weights, evaluation codes, and Goppa codes
Designs, Codes and Cryptography
List decoding codes on Garcia-Stictenoth tower using Gröbner basis
Journal of Symbolic Computation
List decoding of Hermitian codes using Gröbner bases
Journal of Symbolic Computation
Improvements on parameters of algebraic-geometry codes from Hermitian curves
IEEE Transactions on Information Theory
Efficient and generalized pairing computation on Abelian varieties
IEEE Transactions on Information Theory
Multisequences with large linear and k-error linear complexity from Hermitian function fields
IEEE Transactions on Information Theory
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
A new scalar multiplication method suitable for hyperelliptic curve cryptosystems
ICACT'09 Proceedings of the 11th international conference on Advanced Communication Technology - Volume 3
Designs, Codes and Cryptography
On multiplication in finite fields
Journal of Complexity
Codes from Riemann-Roch spaces for y2 = xp - x over GF(p)
International Journal of Information and Coding Theory
A geometric view of decoding AG codes
AAECC'03 Proceedings of the 15th international conference on Applied algebra, algebraic algorithms and error-correcting codes
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
Tabulation of cubic function fields with imaginary and unusual Hessian
ANTS-VIII'08 Proceedings of the 8th international conference on Algorithmic number theory
Algebraic soft-decision decoding of Hermitian codes
IEEE Transactions on Information Theory
Designs, Codes and Cryptography
Generalization of Steane's enlargement construction of quantum codes and applications
IEEE Transactions on Information Theory
Minimum distance decoding of general algebraic geometry codes via lists
IEEE Transactions on Information Theory
Recursive towers of function fields over finite fields
WAIFI'10 Proceedings of the Third international conference on Arithmetic of finite fields
The torsion-limit for algebraic function fields and its application to arithmetic secret sharing
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
Quadratic forms of codimension 2 over certain finite fields of even characteristic
Cryptography and Communications
Stopping set distributions of algebraic geometry codes from elliptic curves
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
Generalised jacobians in cryptography and coding theory
WAIFI'12 Proceedings of the 4th international conference on Arithmetic of Finite Fields
Testers and their applications
Proceedings of the 5th conference on Innovations in theoretical computer science
On the unique representation of very strong algebraic geometry codes
Designs, Codes and Cryptography
Hi-index | 0.36 |
The theory of algebraic function fields has its origins in number theory, complex analysis (compact Riemann surfaces), and algebraic geometry. Since about 1980, function fields have found surprising applications in other branches of mathematics such as coding theory, cryptography, sphere packings and others. The main objective of this book is to provide a purely algebraic, self-contained and in-depth exposition of the theory of function fields. This new edition, published in the series Graduate Texts in Mathematics, has been considerably expanded. Moreover, the present edition contains numerous exercises. Some of them are fairly easy and help the reader to understand the basic material. Other exercises are more advanced and cover additional material which could not be included in the text. This volume is mainly addressed to graduate students in mathematics and theoretical computer science, cryptography, coding theory and electrical engineering.