Applied Algebra, Algebraic Algorithms and Error-Correcting Codes

Table of Contents

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   Book Overview
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   Chapter 1 Supports of a code
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   Chapter 2 Chemical isomerism, a challenge for algebraic combinatorics and for computer science
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   Chapter 3 On algebraic methods in covering radius problems
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   Chapter 4 How lower and upper complexity bounds meet in elimination theory
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   Chapter 5 Bivariate polynomial multiplication patterns
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   Chapter 6 Division of entire functions by polynomial ideals
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   Chapter 7 Variations on minimal codewords in linear codes
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   Chapter 8 On the computation of the radical of polynomial complete intersection ideals
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    Chapter 9 Which families of long binary linear codes have a binomial weight distribution?
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    Chapter 10 The discovery of simple 7-designs with automorphism group PΓL (2, 32)
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    Chapter 11 Fast exponentation in cryptography
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    Chapter 12 On maximal spherical codes I
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    Chapter 13 Formal computation of Galois groups with relative resolvents
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    Chapter 14 A case of automatic theorem proving in Euclidean geometry: the Maclane 8 3 theorem
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    Chapter 15 Isometry classes of indecomposable linear codes
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    Chapter 16 When polynomial equation systems can be “solved” fast?
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    Chapter 17 Using symmetric functions to describe the solution set of a zero dimensional ideal
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    Chapter 18 Triangular systems and factorized Gröbner bases
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    Chapter 19 Computation in algebraic function fields for effective construction of algebraic-geometric codes
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    Chapter 20 Singly-even self-dual codes and Hadamard matrices
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    Chapter 21 Implicitization of curves parameterized by generalized trigonometric polynomials
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    Chapter 22 Randomness properties of partial γ - β planes as LSI test inputs and their implementations
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    Chapter 23 Mixed covering codes with two binary and four ternary coordinates
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    Chapter 24 About approximations of exponentials
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    Chapter 25 A note on normal bases
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    Chapter 26 On the covering radius of long Goppa codes
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    Chapter 27 Integration of multivariate rational functions given by straight-line programs
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    Chapter 28 Polynomial gcd computations over towers of algebraic extensions
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    Chapter 29 Displacements of matrix products
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    Chapter 30 Testing identities of series defined by algebraic partial differential equations
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    Chapter 31 The complexity of formal resolution of linear partial differential equations
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    Chapter 32 A fast parallel implementation of the Berlekamp-Massey algorithm with a 1D systolic array architecture
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    Chapter 33 Tomography of constructible functions
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    Chapter 34 On the determination of formal solutions of a system of partial differential equations
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    Chapter 35 D 4 , E 6 , E 8 and the AGM
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    Chapter 36 Computation of the Galois groups of the resolvent factors for the direct and inverse Galois problems
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    Chapter 37 First integrals and Darboux polynomials of homogeneous linear differential systems