Applied Algebra, Algebraic Algorithms and Error-Correcting Codes

1. Sequences

   1. Iterations of Multivariate Polynomials and Discrepancy of Pseudorandom Numbers

      • Jaime Gutierrez, Domingo Gomez-Perez

      Pages 192-199

   2. Even Length Binary Sequence Families with Low Negaperiodic Autocorrelation

      • Matthew G. Parker

      Pages 200-209

   3. On the Non-existence of (Almost-)Perfect Quaternary Sequences

      • Patrice Parraud

      Pages 210-218

   4. Maximal Periods of x² + c in F_q

      • A. Peinado, F. Montoya, J. Muñoz, A.J. Yuste

      Pages 219-228

   5. On the Aperiodic Correlation Function of Galois Ring m-Sequences

      • P. Udaya1, S. Bozta¢

      Pages 229-238

   6. Euclidean Modules and Multisequence Synthesis

      • Liping Wang

      Pages 239-248

2. Cryptography

   1. On Homogeneous Bent Functions

      • Chris Charnes, Martin Rötteler, Thomas Beth

      Pages 249-259

   2. Partially Identifying Codes for Copyright Protection

      • Sylvia Encheva, Gérard Cohen

      Pages 260-267

   3. On the Generalised Hidden Number Problem and Bit Security of XTR

      • Igor E. Shparlinski

      Pages 268-277

   4. CRYPTIM: Graphs as Tools for Symmetric Encryption

      • Vasyl Ustimenko

      Pages 278-286

3. Algorithms

   1. An Algorithm for Computing Cocyclic Matrices Developed over Some Semidirect Products

      • V. Álvarez, J.A. Armario, M.D. Frau, P. Real

      Pages 287-296

   2. Algorithms for Large Integer Matrix Problems

      • Mark Giesbrecht, Michael Jr. Jacobson, Arne Storjohann

      Pages 297-307

   3. On the Identification of Vertices and Edges Using Cycles

      • Iiro Honkala, Mark G. Karpovsky, Simon Litsyn

      Pages 308-314

4. Algorithms:Decoding

   1. On Algebraic Soft Decision Decoding of Cyclic Binary Codes

      • Vladimir B. Balakirsky

      Pages 315-322

   2. Lifting Decoding Schemes over a Galois Ring

      • Eimear Byrne

      Pages 323-332

   3. Sufficient Conditions on Most Likely Local Sub-codewords in Recursive Maximum Likelihood Decoding Algorithms

      • Tadao Kasami, Hitoshi Tokushige, Yuichi Kaji

      Pages 333-342

   4. A Unifying System-Theoretic Framework for Errors-and-Erasures Reed-Solomon Decoding

      • Margreta Kuijper, Marten van Dijk, Henk Hollmann, Job Oostveen

      Pages 343-352

   5. An Algorithm for Computing Rejection Probability of MLD with Threshold Test over BSC

      • Tadashi Wadayama

      Pages 353-362

5. Algebraic Constructions

   1. Cartan’s Characters and Stairs of Characteristic Sets

      • François Boulier, Sylvain Neut

      Pages 363-372

   2. On the Invariants of the Quotients of the Jacobian of a Curve of Genus 2

      • P. Gaudry, É. Schost

      Pages 373-386

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.

• Algebraic Algorithms
• Algebraic Codes
• Algebraic Curves
• Block Codes
• Code
• Computational Algebra
• Computational Combinatorics
• Computeralgebra
• Cryptographic Codes
• Decoding Algorithms
• Error-correcting Code
• Information
• algorithms
• complexity
• cryptography
• algorithm analysis and problem complexity

• Department of Mathematics, RMIT University, Melbourne, Australia

  Serdar Boztaş

• Department of Computing, Macquarie University, Australia

  Igor E. Shparlinski

Policies and ethics