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The AAECC Symposia Series was started in 1983 by Alain Poli (Toulouse), who, together with R. Desq, D. Lazard, and P. Camion, organized the ?rst conference. Originally the acronym AAECC meant “Applied Algebra and Error-Correcting Codes”. Over the years its meaning has shifted to “Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes”, re?ecting the growing importance of complexity in both decoding algorithms and computational algebra. AAECC aims to encourage cross-fertilization between algebraic methods and their applications in computing and communications. The algebraic orientation is towards ?nite ?elds, complexity, polynomials, and graphs. The applications orientation is towards both theoretical and practical error-correction coding, and, since AAECC 13 (Hawaii, 1999), towards cryptography. AAECC was the ?rst symposium with papers connecting Gr¨obner bases with E-C codes. The balance between theoretical and practical is intended to shift regularly; at AAECC-14 the focus was on the theoretical side. The main subjects covered were: – Codes: iterative decoding, decoding methods, block codes, code construction. – Codes and algebra: algebraic curves, Gr¨obner bases, and AG codes. – Algebra: rings and ?elds, polynomials. – Codes and combinatorics: graphs and matrices, designs, arithmetic. – Cryptography. – Computational algebra: algebraic algorithms. – Sequences for communications.

Error-correcting codes (Information theory) --- Algebra --- Algorithms --- Mathematics --- Physical Sciences & Mathematics --- Data processing --- Codes, Error-correcting (Information theory) --- Error-detecting codes (Information theory) --- Forbidden-combination check (Information theory) --- Self-checking codes (Information theory) --- Mathematics. --- Data encryption (Computer science). --- Coding theory. --- Algorithms. --- Computer science --- Algebra. --- Computer mathematics. --- Coding and Information Theory. --- Symbolic and Algebraic Manipulation. --- Data Encryption. --- Algorithm Analysis and Problem Complexity. --- Computational Mathematics and Numerical Analysis. --- Artificial intelligence --- Automatic control --- Coding theory --- Information theory --- Computer software. --- Cryptology. --- Data processing. --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Software, Computer --- Computer systems --- Data encoding (Computer science) --- Encryption of data (Computer science) --- Computer security --- Cryptography --- Data compression (Telecommunication) --- Digital electronics --- Machine theory --- Signal theory (Telecommunication) --- Computer programming --- Mathematical analysis --- Information theory. --- Computer science—Mathematics. --- Algorism --- Arithmetic --- Communication theory --- Communication --- Cybernetics --- Foundations

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This volume contains selected refereed papers based on lectures presented at the 'Integers Conference 2007', an international conference in combinatorial number theory that was held in Carrollton, Georgia in October 2007. The proceedings include contributions from many distinguished speakers, including George Andrews, Neil Hindman, Florian Luca, Carl Pomerance, Ken Ono and Igor E. Shparlinski. Among the topics considered in these papers are additive number theory, multiplicative number theory, sequences, elementary number theory, theory of partitions, and Ramsey theory.

Combinatorial number theory --- Number theory --- Combinatorial analysis --- Additive Number Theory. --- Combinatorial Game Theory. --- Hypergraphs. --- Multiplicative Number Theory. --- Probabilistic Number Theory. --- Ramsey Theory.