Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 14th International Symposium, AAECC-14, Melbourne, Australia, November 26-30, 2001. [Paperback]

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.Invited Contributions.- The Ubiquity of Reed-Muller Codes.- Self-dual Codes-Theme and Variations.- Design of Differential Space-Time Codes Using Group Theory.- Ideal Error-Correcting Codes: Unifying Algebraic and Number-Theoretic Algorithms.- Block Codes.- Self-dual Codes Using Image Restoration Techniques.- Low Complexity Tail-Biting Trellises of Self-dual codes of Length 24, 32 and 40 over GF(2) and Z4 of Large Minimum Distance.- F q -Linear Cyclic Codes over F q m: DFT Characterization.- Code Constructions.- Cyclic Projective Reed-Muller Codes.- Codes Identifying Sets of Velƒ‘