CONTENTS -- Preface -- List of authors -- The key equation for codes from order domains J. B. Little -- 1. Introduction -- 2. Codes from Order Domains -- 3. Preliminaries on Inverse Systems -- 4. The Key Equation and its Relation to the BMS Algorithm -- Acknowledgements -- References -- A Grobner representation for linear codes M. Borges-Quintana, M. A. Borges-Trenard and E. Mart nez-Moro -- 1. Introduction -- 2. Möller's algorithm -- 3. Gröbner representation of a linear code -- 4. Reduced and border bases -- 4.1. Binary codes -- 5. Applications -- 5.1. Gradient decoding -- 5.2. Permutation equivalent codes -- 5.3. Gröbner codewords for binary codes -- Acknowledgments -- References -- Arcs, minihypers, and the classification of three-dimensional Griesmer codes H. N. Ward -- 1. Introduction -- 2. Codes and the Griesmer bound -- 3. Codes and multisets -- 3.1. Arcs -- 3.2. Combinations -- 4. Minihypers -- 4.1. The Hamada bound -- 4.2. Achievement of the Griesmer bound -- 5. Divisibility -- 6. Three-dimensional Griesmer codes -- 6.1. Orphans -- 6.2. Divisibility -- 6.3. The [92, 3, 80]8 codes -- 6.4. Duality -- Acknowledgment -- References -- Optical orthogonal codes from Singer groups T. L. Alderson and K. E. Mellinger -- 1. Introduction -- 2. Preliminaries -- 3. A construction from arcs in d-flats -- 4. A construction from arcs of higher degree -- 5. Affine constructions -- 6. Conclusion -- Acknowledgments -- References -- Codes over Fp 2 and Fp x Fp, lattices, and theta functions T. Shaska and C. Shor -- 1. Introduction -- 2. Preliminaries -- 2.1. Theta functions over Fp -- 3. Theta functions of codes over R -- 3.1. A MacWilliams identity -- 3.2. A generalization of the symmetric weight enumerator polynomial -- 4. The injectivity of construction A -- 4.1. The case p = 2 -- 4.2. The case p > 2 -- Acknowledgment -- References.

Goppa codes and Tschirnhausen modules D. Coles and E. Previato -- Introduction -- 1. Goppa Codes and rank-2 Vector Bundles -- 2. The Klein Curve as Cover -- 3. The Tschirnhausen Module of the Cover -- 4. Goppa Codes and Adeles -- 4.1. Adeles and pseudo-differentials -- 4.2. Goppa codes and adeles -- Acknowledgements -- References -- Remarks on s-extremal codes J.-L. Kim -- 1. Introduction -- 2. s-Extremal Additive F4 Codes -- 3. s-Extremal Binary Codes -- 4. Conclusion -- Acknowledgments -- References -- Automorphism groups of generalized Reed-Solomon codes D. Joyner, A. Ksir and W. Traves -- 1. Introduction -- 2. AG codes and GRS codes -- 3. Automorphisms -- 4. Examples -- 5. Structure of the representations -- References -- About the code equivalence I. G. Bouyukliev -- 1. Introduction -- 2. Codes and binary matrices -- 2.1. Equivalence of linear codes -- 2.2. Isomorphism of binary matrices -- 2.3. The connection between equivalence of linear codes and isomorphism of binary matrices -- 3. Orbits, partitions, invariants -- 3.1. Orbits -- 3.2. Partitions, ordered partitions -- 3.3. Definition of invariants -- 3.4. Properties of partitions induced by invariants -- 3.5. Invariants of columns and rows -- 4. Main algorithm -- 4.1. Additional invariants -- 5. Efficiency and storage requirements -- References -- Permutation decoding for binary self-dual codes from the graph Qn where n is even J. D. Key and P. Seneviratne -- 1. Introduction -- 2. Background and terminology -- 3. Binary codes of cubic graphs -- 4. 3-PD-sets -- 5. Discussion -- References -- The sum-product algorithm on small graphs M. E. O'Sullivan, J. Brevik and R. Wolski -- 1. Introduction -- 2. Experimental Results -- 3. Analysis of the Sum-Product Algorithm -- Bipartite Graphs -- The Sum-Product Algorithm -- 4. Examples -- 2 bits n checks -- 4-Choose-2.

3-to-1 covers of the complete 2-bits-3-checks graph -- Degradation of performance with the coarse termination criterion -- 5. Concluding Remarks -- References -- On the extremal graph theory for directed graphs and its cryptographical applications V. A. Ustimenko -- 1. Introduction -- 2. Binary relations, related rainbow-like graphs and algorithms -- 2.1. Binary relations and special colorings -- 2.2. General symmetric algorithm -- 2.3. Symbolic computations and public keys -- 2.4. Coding theory, other applications -- 3. The incidence structures defined over commutative rings -- 4. Symmetric encryption, algorithms related to graphs RF(n,K) -- 4.1. The encryption algorithm -- 4.2. Decryption procedure -- 4.3. Examples -- 5. Public keys -- 6. Other algebraic parallelotopic graphs -- 7. Remarks on implementation -- References -- Fast arithmetic on hyperelliptic curves via continued fraction expansions M. J. Jacobson, Jr., R. Scheidler and A. Stein -- 1. Introduction and Motivation -- 2. Continued Fraction Expansions -- 3. Hyperelliptic Curves -- 3.1. Imaginary Curves -- 3.2. Unusual Curves -- 3.3. Real Curves -- 4. Reduced Ideals and Divisors -- 4.1. Imaginary Curves -- 4.2. Unusual Curves -- 4.3. Real Curves -- 5. Reduction and Baby Steps -- 6. Giant Steps and the Idea of NUCOMP -- 6.1. Imaginary Curves -- 6.2. Unusual Curves -- 6.3. Real Curves -- 7. NUCOMP -- 8. Giant Steps with NUCOMP -- 9. NUCOMP Algorithms -- 10. An Extra Reduced Divisor -- 11. Numerical Results -- 11.1. Binary Exponentiation -- 11.2. Key Exchange -- 12. Conclusions -- References -- The number of inequivalent binary self-orthogonal codes of dimension 6 X.-D. Hou -- 1. Introduction -- 2. Method of Computation -- Appendix. Tables -- References.