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Ever since the seminal work of Goppa on algebraic-geometry codes, rational points on algebraic curves over finite fields have been an important research topic for algebraic geometers and coding theorists. The focus in this application of algebraic geometry to coding theory is on algebraic curves over finite fields with many rational points (relative to the genus). Recently, the authors discovered another important application of such curves, namely to the construction of low-discrepancy sequences. These sequences are needed for numerical methods in areas as diverse as computational physics and mathematical finance. This has given additional impetus to the theory of, and the search for, algebraic curves over finite fields with many rational points. This book aims to sum up the theoretical work on algebraic curves over finite fields with many rational points and to discuss the applications of such curves to algebraic coding theory and the construction of low-discrepancy sequences.

Curves, Algebraic. --- Finite fields (Algebra) --- Rational points (Geometry) --- Coding theory. --- Data compression (Telecommunication) --- Digital electronics --- Information theory --- Machine theory --- Signal theory (Telecommunication) --- Computer programming --- Points, Rational (Geometry) --- Arithmetical algebraic geometry --- Modular fields (Algebra) --- Algebra, Abstract --- Algebraic fields --- Galois theory --- Modules (Algebra) --- Algebraic curves --- Algebraic varieties

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Mathematics

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This book constitutes the refereed proceedings of the Second International Workshop on Coding and Cryptology, IWCC 2009, held in Zhangjiajie, China, in June 2009. The 21 revised full technical papers, except one, are contributed by the invited speakers of the workshop. The papers were carefully selected during two rounds of reviewing and improvement for inclusion in the volume and address all aspects of coding theory, cryptology and related areas - such as combinatorics - theoretical or applied. Topics addressed are coding theory, secure codes, hash functions, combinatorics, boolean functions, authentication, cryptography, protocols, sequences, and secure communications.

Coding theory --- Cryptography --- Algebra --- Mathematics --- Physical Sciences & Mathematics --- Coding theory. --- Computational complexity. --- Computer networks. --- Computer science. --- Data encryption (Computer science) --- Informatics --- Communication systems, Computer --- Computer communication systems --- Data networks, Computer --- ECNs (Electronic communication networks) --- Electronic communication networks --- Networks, Computer --- Teleprocessing networks --- Complexity, Computational --- Data encoding (Computer science) --- Encryption of data (Computer science) --- Computer communication systems. --- Data encryption (Computer science). --- Computer science --- Computer Science. --- Data Encryption. --- Coding and Information Theory. --- Discrete Mathematics in Computer Science. --- Computer Communication Networks. --- Mathematics. --- Science --- Data compression (Telecommunication) --- Digital electronics --- Information theory --- Machine theory --- Signal theory (Telecommunication) --- Computer programming --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Computer security --- Data transmission systems --- Digital communications --- Electronic systems --- Information networks --- Telecommunication --- Cyberinfrastructure --- Network computers --- Distributed processing --- Cryptology. --- Information theory. --- Computer science—Mathematics. --- Communication theory --- Communication --- Cybernetics

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Ergodic theory. Information theory --- Discrete mathematics --- Computer science --- Computer architecture. Operating systems --- coderen --- DES (data encryption standard) --- discrete wiskunde --- cryptologie --- informatica --- computernetwerken --- informatietheorie