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Applied algebra, Algebraic Algorithms by Serdar Boztas and Hsiao-feng Lu



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Applied algebra, Algebraic Algorithms by Serdar Boztas and Hsiao-feng Lu . 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. The 33 revised full papers presented together with 8 invited papers were carefully reviewed and selected from 61 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.
The AAECC Symposia Series was started in 1983 by Alain Poli (Toulouse), who, together with R. Desq, D. Lazard and P. Camion, organized the first 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,” reflecting the growing importance of complexity, particularly for decoding algorithms. During the AAECC-12 symposium the conference committee decided to enforce the theory and practice of the coding side as well as the cryptographic aspects. Algebra was conserved, as in the past, but slightly more oriented to algebraic geometry codes, finite fields, complexity, polynomials, and graphs.

Applied algebra, Algebraic Algorithms by Serdar Boztas and Hsiao-feng Lu cover the following topics.

  • 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 Hajime Watanabe, Kazuto Ogawa, and Hideki Imai
    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
    Silvana Medo?s and Serdar Bozta¸s
    A Note on a Class of Quadratic Permutations over F2n
    Constructions of Orthonormal Lattices and Quaternion Division
    Algebras for Totally Real Number Fields
    Quaternary Plotkin Constructions and Quaternary Reed-Muller Codes
    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
    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

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