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Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 14th International Symposium, AAECC-14 Melbourne, Australia, November 26–30, 2001 Proceedings

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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.

Author(s): James L. Massey (auth.), Serdar Boztaş, Igor E. Shparlinski (eds.)
Series: Lecture Notes in Computer Science 2227
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2001

Language: English
Pages: 404
Tags: Coding and Information Theory; Symbolic and Algebraic Manipulation; Data Encryption; Algorithm Analysis and Problem Complexity; Computational Mathematics and Numerical Analysis

The Ubiquity of Reed-Muller Codes....Pages 1-12
Self-dual Codes-Theme and Variations....Pages 13-21
Design of Differential Space-Time Codes Using Group Theory....Pages 22-35
Ideal Error-Correcting Codes: Unifying Algebraic and Number-Theoretic Algorithms....Pages 36-45
Self-dual Codes Using Image Restoration Techniques....Pages 46-56
Low Complexity Tail-Biting Trellises of Self-dual codes of Length 24, 32 and 40 over GF (2) and Z4 of Large Minimum Distance....Pages 57-66
F q -Linear Cyclic Codes over F q m : DFT Characterization....Pages 67-76
Cyclic Projective Reed-Muller Codes....Pages 77-81
Codes Identifying Sets of Vertices....Pages 82-91
Duality and Greedy Weights of Linear Codes and Projective Multisets....Pages 92-101
Type II Codes over IF 2 r....Pages 102-111
On Senary Simplex Codes....Pages 112-121
Optimal Double Circulant Z4-Codes....Pages 122-128
Constructions of Codes from Number Fields....Pages 129-140
On Generalized Hamming Weights for Codes over Finite Chain Rings....Pages 141-150
Information Rates and Weights of Codes in Structural Matrix Rings....Pages 151-158
On Hyperbolic Codes....Pages 159-171
On Fast Interpolation Method for Guruswami-Sudan List Decoding of One-Point Algebraic-Geometry Codes....Pages 172-181
Computing the Genus of a Class of Curves....Pages 182-191
Iterations of Multivariate Polynomials and Discrepancy of Pseudorandom Numbers....Pages 192-199
Even Length Binary Sequence Families with Low Negaperiodic Autocorrelation....Pages 200-209
On the Non-existence of (Almost-)Perfect Quaternary Sequences....Pages 210-218
Maximal Periods of x 2 + c in F q ....Pages 219-228
On the Aperiodic Correlation Function of Galois Ring m -Sequences....Pages 229-238
Euclidean Modules and Multisequence Synthesis....Pages 239-248
On Homogeneous Bent Functions....Pages 249-259
Partially Identifying Codes for Copyright Protection....Pages 260-267
On the Generalised Hidden Number Problem and Bit Security of XTR....Pages 268-277
CRYPTIM: Graphs as Tools for Symmetric Encryption....Pages 278-286
An Algorithm for Computing Cocyclic Matrices Developed over Some Semidirect Products....Pages 287-296
Algorithms for Large Integer Matrix Problems....Pages 297-307
On the Identification of Vertices and Edges Using Cycles....Pages 308-314
On Algebraic Soft Decision Decoding of Cyclic Binary Codes....Pages 315-322
Lifting Decoding Schemes over a Galois Ring....Pages 323-332
Sufficient Conditions on Most Likely Local Sub-codewords in Recursive Maximum Likelihood Decoding Algorithms....Pages 333-342
A Unifying System-Theoretic Framework for Errors-and-Erasures Reed-Solomon Decoding....Pages 343-352
An Algorithm for Computing Rejection Probability of MLD with Threshold Test over BSC....Pages 353-362
Cartan’s Characters and Stairs of Characteristic Sets....Pages 363-372
On the Invariants of the Quotients of the Jacobian of a Curve of Genus 2....Pages 373-386
Algebraic Constructions for PSK Space-Time Coded Modulation....Pages 387-396