Applied Algebra, Algebraic Algorithms and Error-Correcting Codes

ISBN-13: 9783540772231 / Angielski / Miękka / 2007 / 388 str.

Serdar Boztas

Opis

This book constitutes the refereed proceedings of the 17th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-17, held in Bangalore, India, in December 2007. 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.

Spis treści

Invited Contributions.- List Decoding and Pseudorandom Constructions.- A Survey of Recent Attacks on the Filter Generator.- Iterative List Decoding of LDPC Codes.- Inverted Edwards Coordinates.- Spectra of Boolean Functions, Subspaces of Matrices, and Going Up Versus Going Down.- Efficient List Decoding of Explicit Codes with Optimal Redundancy.- Algebraic Structure Theory of Tail-Biting Trellises.- Nice Codes from Nice Curves.- Regular Contributions.- Generalized Sudan’s List Decoding for Order Domain Codes.- Bent Functions and Codes with Low Peak-to-Average Power Ratio for Multi-Code CDMA.- Determining the Nonlinearity of a New Family of APN Functions.- An Improvement of Tardos’s Collusion-Secure Fingerprinting Codes with Very Short Lengths.- Space-Time Codes from Crossed Product Algebras of Degree 4.- On Non-randomness of the Permutation After RC4 Key Scheduling.- Correctable Errors of Weight Half the Minimum Distance Plus One for the First-Order Reed-Muller Codes.- Fault-Tolerant Finite Field Computation in the Public Key Cryptosystems.- A Note on a Class of Quadratic Permutations over .- Constructions of Orthonormal Lattices and Quaternion Division Algebras for Totally Real Number Fields.- Quaternary Plotkin Constructions and Quaternary Reed-Muller Codes.- Joint Source-Cryptographic-Channel Coding Based on Linear Block Codes.- On the Key-Privacy Issue of McEliece Public-Key Encryption.- Lattices for Distributed Source Coding: Jointly Gaussian Sources and Reconstruction of a Linear Function.- Linear Complexity and Autocorrelation of Prime Cube Sequences.- The “Art of Trellis Decoding” Is NP-Hard.- On the Structure of Inversive Pseudorandom Number Generators.- Subcodes of Reed-Solomon Codes Suitable for Soft Decoding.- Normalized Minimum Determinant Calculation for Multi-block and Asymmetric Space-Time Codes.- On the Computation of Non-uniform Input for List Decoding on Bezerra-Garcia Tower.- Dense MIMO Matrix Lattices — A Meeting Point for Class Field Theory and Invariant Theory.- Secure Cross-Realm Client-to-Client Password-Based Authenticated Key Exchange Against Undetectable On-Line Dictionary Attacks.- Links Between Discriminating and Identifying Codes in the Binary Hamming Space.- Construction of Rotation Symmetric Boolean Functions on Odd Number of Variables with Maximum Algebraic Immunity.- A Path to Hadamard Matrices.- The Tangent FFT.- Novel Algebraic Structure for Cyclic Codes.- Distribution of Trace Values and Two-Weight, Self-orthogonal Codes over GF(p,2).- Generalized Rotation Symmetric and Dihedral Symmetric Boolean Functions ? 9 Variable Boolean Functions with Nonlinearity 242.- On Quasi-cyclic Codes over Integer Residue Rings.- Extended Norm-Trace Codes with Optimized Correction Capability.- On Generalized Hamming Weights and the Covering Radius of Linear Codes.- Homomorphic Encryptions of Sums of Groups.