appliedalgebra, algebraicalgorithms, and error-correctingcodes : 13thinternationalsymposium, Aaecc-13, Honolulu, Hawaii, Usa, November 15-19, 1999 : Proceedings by Aaecc-13 (1999 : Honolulu, Hawaii); Fossorier, M...
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appliedalgebra, algebraicalgorithms, and error-correctingcodes : 13thinternationalsymposium, Aaecc-13, Honolulu, Hawaii, Usa, November 15-19, 1999 : Proceedings by Aaecc-13 (1999 : Honolulu, Hawaii); Fossorier, Marc, 1964-; published by Berlin ; New York : Springer
the proceedings contain 28 papers. the topics discussed include: the order bound for toric codes;from the Euclidean algorithm for solving a key equation for dual Reed-Solomon codes to the Berlekamp-Massey algorithm;op...
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ISBN:
(纸本)3642021808
the proceedings contain 28 papers. the topics discussed include: the order bound for toric codes;from the Euclidean algorithm for solving a key equation for dual Reed-Solomon codes to the Berlekamp-Massey algorithm;optimal bipartite Ramanujan graphs from balanced incomplete block designs: their characterizations and applications to expander/LDPC codes;simulation of the sum-product algorithm using stratified sampling;a systems theory approach to periodically time-varying convolutional codes by means of their invariant equivalent;a non-abelian group based on block upper triangular matrices with cryptographic applications;very-efficient anonymous password-authenticated key exchange and its extensions;efficient constructions of deterministic encryption from hybrid encryption and code-based PKE;and noisy interpolation of multivariate sparse polynomials in finite fields.
the proceedings contain 39 papers. the topics discussed include: list decoding and pseudorandom constructions;a survey of recent attacks on the filter generator;iterative list decoding LDPC codes;inverted Edwards coor...
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ISBN:
(纸本)9783540772231
the proceedings contain 39 papers. the topics discussed include: list decoding and pseudorandom constructions;a survey of recent attacks on the filter generator;iterative list decoding 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 redudancy;algebraic structure theory of tail-biting Trellises;nice codes from nice curves;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;and subcodes of Reed-Solomon codes suitable for soft decoding.
We argue that the symmetries of a property being tested play a central role in property testing. We support this assertion in the context of algebraic functions, by examining properties of functions mapping a vector s...
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ISBN:
(纸本)9781605604657
We argue that the symmetries of a property being tested play a central role in property testing. We support this assertion in the context of algebraic functions, by examining properties of functions mapping a vector space K~n over a field K to a subfield F. We consider (F-)linear properties that are invariant under linear transformations of the domain and prove that an O(1)-local "characterization" is a necessary and sufficient condition for O(1) -local testability, when |K| = O(1). (A local characterization of a property is a definition of a property in terms of local constraints satisfied by functions exhibiting a property.) For the subclass of properties that are invariant under affine transformations of the domain, we prove that the existence of a single O(1)-local constraint implies O(1)-local testability. these results generalize and extend the class of algebraic properties, most notably linearity and low-degree-ness, that were previously known to be testable. In particular, the extensions include properties satisfied by functions of degree linear in n that turn out to be O(1)-locally testable. Our results are proved by introducing a new notion that we term "formal characterizations". Roughly this corresponds to characterizations that are given by a single local constraint and its permutations under linear transformations of the domain. Our main testing result shows that local formal characterizations essentially imply local testability. We then investigate properties that are linear-invariant and attempt to understand their local formal characterizability. Our results here give coarse upper and lower bounds on the locality of constraints and characterizations for linear-invariant properties in terms of some structural parameters of the property we introduce. the lower bounds rule out any characterization, while the upper bounds give formal characterizations. Combining the two gives a test for all linear-invariant properties with local characterizations. We be
the proceedings contain 32 papers. the topics discussed include: on bent and highly nonlinear balanced/resilient functions and their algebraic immunities;quantum period reconstruction of binary sequences;a general fra...
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ISBN:
(纸本)3540314237
the proceedings contain 32 papers. the topics discussed include: on bent and highly nonlinear balanced/resilient functions and their algebraic immunities;quantum period reconstruction of binary sequences;a general framework for applying FGLM techniques to linear codes;the solutions of the third power sum equation for Niho type decimations;computing Gröbner bases for vanishing ideals of finite sets of points;a fast calculus for the linearizing attack and its application to an attack on KASUMI;on achieving chosen ciphertext security with decryption errors;a short random fingerprinting code against a small number of pirates;and a general formulation of algebraic and fast correlation attacks based on dedicated sample decimation.
the proceedings contain 27 papers. the special focus in this conference is on appliedalgebra, algebraic algorithms and error-correcting codes. the topics include: Cryptography and the methodology of provable security...
ISBN:
(纸本)3540401113
the proceedings contain 27 papers. the special focus in this conference is on appliedalgebra, algebraic algorithms and error-correcting codes. the topics include: Cryptography and the methodology of provable security;dynamical systems generated by rational functions;homotopy methods for equations over finite fields;the Jacobi model of an elliptic curve and side-channel analysis;fast point multiplication on elliptic curves through isogenies;an optimized algebraic method for higher order differential attack;copyright control and separating systems;unconditionally secure homomorphic pre-distributed commitments;relative duality in MacWilliams identity;good expander graphs and expander codes;on the covering radius of certain cyclic codes;the second and third generalized hamming weights of algebraic geometry codes;performance analysis of m-PSK signal constellations in Riemannian varieties;improvements to evaluation codes and new characterizations of ARF semigroups and fast decomposition of polynomials with known Galois group.
We study errorcorrectingcodes over algebraic surfaces. We give a construction of linear errorcorrectingcodes over an arbitrary algebraic surface and then we focus on linear codes over ruled surfaces. At the end we...
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ISBN:
(纸本)3540401113
We study errorcorrectingcodes over algebraic surfaces. We give a construction of linear errorcorrectingcodes over an arbitrary algebraic surface and then we focus on linear codes over ruled surfaces. At the end we discuss another approach to getting codes over algebraic surfaces using sections of rank two bundles. the new codes are not linear but do have a group structure.
the proceedings contain 40 papers. the special focus in this conference is on Block codes, Code Constructions, Rings, Fields, algebraic Geometry codes and Sequences. the topics include: the ubiquity of reed-Muller cod...
ISBN:
(纸本)9783540456247
the proceedings contain 40 papers. the special focus in this conference is on Block codes, Code Constructions, Rings, Fields, algebraic Geometry codes and Sequences. the topics include: the ubiquity of reed-Muller codes;design of differential space-time codes using group theory;self-dual codes using image restoration techniques;duality and greedy weights of linear codes and projective multisets;constructions of codes from number fields;on generalized hamming weights for codes over finite chain rings;information rates and weights of codes in structural matrix rings;on fast interpolation method for Guruswami-Sudan list decoding of one-point algebraic-geometry codes;computing the genus of a class of curves;iterations of multivariate polynomials and discrepancy of pseudorandom numbers;even length binary sequence families with low negaperiodic autocorrelation;on the aperiodic correlation function of Galois ring m-sequences;Euclidean modules and multisequence synthesis;partially identifying codes for copyright protection;on the generalised hidden number problem and bit security of XTR;graphs as tools for symmetric encryption;an algorithm for computing cocyclic matrices developed over some semidirect products;algorithms for large integer matrix problems;on the identification of vertices and edges using cycles;on algebraic soft decision decoding of cyclic binary codes;lifting decoding schemes over a Galois ring;sufficient conditions on most likely local sub-codewords in recursive maximum likelihood decoding algorithms and a unifying system-theoretic framework for errors-and-erasures reed-Solomon decoding.
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