Lecture Notes in Computer Science

14th International Symposium, AAECC-14, Melbourne, Australia, November 26-30, 2001. Proceedings

By: Serdar Boztas (Editor), Igor E. Shparlinski (Editor)

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Paperback | 12 November 2001

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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.

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Non-Fiction Mathematics Algebra Reference, Information & Interdisciplinary Subjects Research & Information Information theory Computing & I.T.Databases Data Capture & Analysis Medicine Medicine in General Computer Science

Computer Programming & Software Development Algorithms & Data Structures Applied Mathematics Calculus & Mathematical Analysis Numerical Analysis Computer Security Data Encryption

Invited Contributions
The Ubiquity of Reed-Muller Codes	p. 1
Self-dual Codes-Theme and Variations	p. 13
Design of Differential Space-Time Codes Using Group Theory	p. 22
Ideal Error-Correcting Codes: Unifying Algebraic and Number-Theoretic Algorithms	p. 36
Block Codes
Self-dual Codes Using Image Restoration Techniques	p. 46
Low Complexity Tail-Biting Trellises of Self-dual Codes of Length 24, 32and 40 over GF(2) and Z(4) of Large Minimum Distance	p. 57
F(q)-Linear Cyclic Codes over F(q)(m) : DFT Characterization	p. 67
Code Constructions
Cyclic Projective Reed-Muller Codes	p. 77
Codes Identifying Sets of Vertices	p. 82
Duality and Greedy Weights of Linear Codes and Projective Multisets	p. 92
Codes and Algebra: Rings and Fields
Type II Codes over F(2)(r)	p. 102
On Senary Simplex Codes	p. 112
Optimal Double Circulant Z4-Codes	p. 122
Constructions of Codes from Number Fields	p. 129
On Generalized Hamming Weights for Codes over Finite Chain Rings	p. 141
Information Rates and Weights of Codes in Structural Matrix Rings	p. 151
Codes and Algebra: Algebraic Geometry Codes
On Hyperbolic Codes	p. 159
On Fast Interpolation Method for Guruswami-Sudan List Decoding of One-Point Algebraic-Geometry Codes	p. 172
Computing the Genus of a Class of Curves	p. 182
Sequences
Iterations of Multivariate Polynomials and Discrepancy of Pseudorandom Numbers	p. 192
Even Length Binary Sequence Families with Low Negaperiodic Autocorrelation	p. 200
On the Non-existence of (Almost-)Perfect Quaternary Sequences	p. 210
Maximal Periods of x(2) + c in F(q)	p. 219
On the Aperiodic Correlation Function of Galois Ring m-Sequences	p. 229
Euclidean Modules and Multisequence Synthesis	p. 239
Cryptography
On Homogeneous Bent Functions	p. 249
Partially Identifying Codes for Copyright Protection	p. 260
On the Generalised Hidden Number Problem and Bit Security of XTR	p. 268
CRYPTIM: Graphs as Tools for Symmetric Encryption	p. 278
Algorithms
An Algorithm for Computing Cocyclic Matrices Developed over Some Semidirect Products	p. 287
Algorithms for Large Integer Matrix Problems	p. 297
On the Identification of Vertices and Edges Using Cycles	p. 308
Algorithms: Decoding
On Algebraic Soft Decision Decoding of Cyclic Binary Codes	p. 315
Lifting Decoding Schemes over a Galois Ring	p. 323
Sufficient Conditions on Most Likely Local Sub-codewords in Recursive Maximum Likelihood Decoding Algorithms	p. 333
A Unifying System-Theoretic Framework for Errors-and-Erasures Reed-Solomon Decoding	p. 343
An Algorithm for Computing Rejection Probability of MLD with Threshold Test over BSC	p. 353
Algebraic Constructions
Cartan's Characters and Stairs of Characteristic Sets	p. 363
On the Invariants of the Quotients of the Jacobian of a Curve of Genus 2	p. 373
Algebraic Constructions for PSK Space-Time Coded Modulation
Author Index	p. 397
Table of Contents provided by Publisher. All Rights Reserved.

Lecture Notes in Computer Science

14th International Symposium, AAECC-14, Melbourne, Australia, November 26-30, 2001. Proceedings

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