Applied Algebra, Algebraic Algorithms and Error-Correcting Codes

1. Front Matter

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2. Codes

   1. The Order Bound for Toric Codes

      • Peter Beelen, Diego Ruano

      Pages 1-10

   2. An Extension of the Order Bound for AG Codes

      • Iwan Duursma, Radoslav Kirov

      Pages 11-22

   3. Sparse Numerical Semigroups

      • C. Munuera, F. Torres, J. Villanueva

      Pages 23-31

   4. From the Euclidean Algorithm for Solving a Key Equation for Dual Reed–Solomon Codes to the Berlekamp–Massey Algorithm

      • Maria Bras-Amorós, Michael E. O’Sullivan

      Pages 32-42

   5. Rank for Some Families of Quaternary Reed-Muller Codes

      • Jaume Pernas, Jaume Pujol, Mercè Villanueva

      Pages 43-52

   6. Optimal Bipartite Ramanujan Graphs from Balanced Incomplete Block Designs: Their Characterizations and Applications to Expander/LDPC Codes

      • Tom Høholdt, Heeralal Janwal

      Pages 53-64

   7. Simulation of the Sum-Product Algorithm Using Stratified Sampling

      • John Brevik, Michael E. O’Sullivan, Anya Umlauf, Rich Wolski

      Pages 65-72

   8. A Systems Theory Approach to Periodically Time-Varying Convolutional Codes by Means of Their Invariant Equivalent

      • Joan-Josep Climent, Victoria Herranz, Carmen Perea, Virtudes Tomás

      Pages 73-82

   9. On Elliptic Convolutional Goppa Codes

      • José Ignacio Iglesias Curto

      Pages 83-91

   10. The Minimum Hamming Distance of Cyclic Codes of Length 2p ^s

       • Hakan Özadam, Ferruh Özbudak

       Pages 92-100

   11. There Are Not Non-obvious Cyclic Affine-invariant Codes

       • José Joaquín Bernal, Ángel del Río, Juan Jacobo Simón

       Pages 101-106

   12. On Self-dual Codes over Z ₁₆

       • Kiyoshi Nagata, Fidel Nemenzo, Hideo Wada

       Pages 107-116

3. Cryptography

   1. A Non-abelian Group Based on Block Upper Triangular Matrices with Cryptographic Applications

      • Rafael Álvarez, Leandro Tortosa, José Vicent, Antonio Zamora

      Pages 117-126

   2. Word Oriented Cascade Jump σ−LFSR

      • Guang Zeng, Yang Yang, Wenbao Han, Shuqin Fan

      Pages 127-136

   3. On Some Sequences of the Secret Pseudo-random Index j in RC4 Key Scheduling

      • Riddhipratim Basu, Subhamoy Maitra, Goutam Paul, Tanmoy Talukdar

      Pages 137-148

   4. Very-Efficient Anonymous Password-Authenticated Key Exchange and Its Extensions

      • SeongHan Shin, Kazukuni Kobara, Hideki Imai

      Pages 149-158

   5. Efficient Constructions of Deterministic Encryption from Hybrid Encryption and Code-Based PKE

      • Yang Cui, Kirill Morozov, Kazukuni Kobara, Hideki Imai

      Pages 159-168

4. Algebra

   1. Noisy Interpolation of Multivariate Sparse Polynomials in Finite Fields

      • Álvar Ibeas, Arne Winterhof

      Pages 169-178

   2. New Commutative Semifields and Their Nuclei

      • Jürgen Bierbrauer

      Pages 179-185

This book constitutes the refereed proceedings of the 18th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-18, held in Tarragona, Spain, in June 2009. The 22 revised full papers presented together with 7 extended absstracts were carefully reviewed and selected from 50 submissions. Among the subjects addressed are block codes, including list-decoding algorithms; algebra and codes: rings, fields, algebraic geometry codes; algebra: rings and fields, polynomials, permutations, lattices; cryptography: cryptanalysis and complexity; computational algebra: algebraic algorithms and transforms; sequences and boolean functions.

• Berlekamp-Messey
• Hamming distance
• Hjelmslev geometry
• Permutation
• Ramanujan Graphs
• Reed-Muller
• algebra
• algorithms
• complexity
• cyclic codes
• dual RS codes
• elliptic curves
• encryption
• self-dual codes
• toric codes

• Departament d’Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Tarragona, Spain

  Maria Bras-Amorós

• Department of Mathematics, The Technical University of Denmark, Lyngby, Denmark

  Tom Høholdt

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