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检索条件"任意字段=17th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes"

共 33 条记录，以下是21-30 订阅

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A zero-test and an interpolation algorithm for the shifted sparse polynomials 10th

A zero-test and an interpolation algorithm for the shifted s...

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10th international symposium on applied algebra, algebraic algorithms and error-correcting codes, AAECC - 10 1993

作者： Grigoriev, Dims Karpinski, Marek Dept of Computer Science The Pennsylvania State University University ParkPA16802 United States Dept of Computer Science University of Bonn International Computer Science Institute 5300 Bonn 1 BerkeleyCA United States Dept of Computer Science University of Bonn Germany

ISBN: (纸本)9783540566861

Recall that a polynomial f ∈ F [X1,…,Xn] is t-sparse, if f = ∑ αIXI contains at most t terms. In [BT 88], [GKS 90] (see also [GK 87] and [Ka 89]) the problem of interpolation of t-sparse polynomial given by a black-box for its evaluation has been solved. In this paper we shall assume that F is a field of characteristic zero. One can consider a t-sparse polynomial as a polynomial represented by a straight-line program or an arithmetic circuit of the depth 2 where on the first level there are multiplications with unbounded fan-in and on the second level there is an addition with fan-in t. In the present paper we consider a generalization of the notion of sparsity, namely we say that a polynomial g(X1,…,Xn) ∈ F[X1,…, Xn] is shifted t-sparse if for a suitable nonsingular n x n matrix A and a vector B the polynomial g(A(X1,…,Xn)T + B) is t-sparse. One could consider g as being represented by a straight-line program of the depth 3 where on the first level (with the fan-in n + 1) a linear transformation A(X1,…,Xn) + B is computed. One could also consider a shifted t-sparse polynomial as t-sparse with respect to other coordinates (Y1,…,Yn)T=A(X1,…,Xn)T + B. We assume that a shifted t-sparse polynomial g is given by a black-box and the problem we consider is to construct a transformation A(X1,…,Xn) + B. As the complexity of the designed below algorithm (see the theorem in which we describe the variety of all possible A, B and the corresponding t-sparse representations of g(A(X1,…,Xn)T + B)) depends on dn4 where d is the degree of g, we could first interpolate g within time dO(n) and suppose that g is given explicitly. It would be interesting to get rid of d in the complexity bounds as it is usually done in the interpolation of sparse polynomials ([BT 88], [GKS 90], [Ka 89]). the main technical tool we rely on is the criterium of t-sparsity based on Wronskian ([GKS 91], [GKS 92]), the latter criterium has a parametrical nature (so we can select t-sparse polynomials from a giv

关键词： Polynomials

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9th international symposium on applied algebra, algebraic algorithms and error-correcting codes, AAECC 1991

9th International Symposium on Applied Algebra, Algebraic Al...

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9th international symposium on applied algebra, algebraic algorithms and error-correcting codes, AAECC 1991

ISBN: (纸本)9783540545224

the proceedings contain 45 papers. the special focus in this conference is on applied algebra. the topics include: algorithms for the shape of semialgebraic sets. a new approach;on the parameters of algebraic geometric cedes;on wiedemann's method of solving sparse linear systems;fast algorithms for decoding orthogonal and related codes;jacobian matrices and constructions in algebra;homogenity, pseudo-homogenity, and grobner basis computations;arithmetic on non-supersingular elliptic curves;implementing some algorithms of kantor;computing roadmaps of general semi-algebraic sets;an improved sign determination algorithm;buchberger algorithm and integer programming;new systolic architectures for cyclic code encoding;algebraic constructions of efficient broadcast networks;error-correction for WIMs and WUMs;some constructions in rings of differential polynomials;an algorithm for the computation of the radical of an ideal in the ring of polynomials;polynomial-time construction of spherical codes;algorithms for a multiple algebraic extension ii;on the orphans and covering radius of the reed-muller codes;a joint authentication and encryption scheme based on algebraic coding theory;some results on linear unequal-error-protection codes specified by their generator matrix;an ackermannian polynomial idealsome undecidability results for weakly confluent monadic string-rewriting systems;calculating multidimensional symmetric functions using jacobi's formula;multivariate sturm theory;binary spherical geometric codes;an algebraic construction of generalized beenkefs cedes;improving the time complexity of the computation of irreducible and primitive polynomials in finite fields;completely transitive codes and distance transitive graphs.

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Concurrent error detection in sequential circuits using convolutional codes 9th

Concurrent error detection in sequential circuits using conv...

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9th international symposium on applied algebra, algebraic algorithms and error-correcting codes, AAECC 1991

作者： Holmquist, Lawrence P. Kinney, L.L. International Business Machines Corporation Route 17C OwegoNY13827 United States Department of Electrical Engineering University of Minnesota 200 Union Street SE #4-178 MinneapolisMN55455 United States

ISBN: (纸本)9783540545224

Concurrent error detection schemes in digital systems are often based upon error-detecting codes. In [9], we presented a methodology for encoding the states of sequential machines using convolutional codes for on-line detection of sequencing errors. In conjunction with this methodology, we defined an equivalence relation on convolutional codes that exhaustively characterizes the possible transient error detection capabilities and complexities of sequential machine realizations based upon convolutional codes. In this paper, we determine the number of equivalence classes of (n, k, 1) convolutional codes generated by minimal encoders requiring k memory elements and provide a procedure for generating representatives from each equivalence class. © 1991, Springer Verlag. All rights reserved.

关键词： Convolutional codes

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the 2-nd generalized hamming weight of double-error correcting binary BCH codes and their dual codes 9th

The 2-nd generalized hamming weight of double-error correcti...

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9th international symposium on applied algebra, algebraic algorithms and error-correcting codes, AAECC 1991

作者： Chung, Habong Department of Electrical and Computer Engineering State University of New York at Buffalo BuffaloNY14260 United States

ISBN: (纸本)9783540545224

the generalized Hamming weight of a linear code is a new notion of higher dimensional Hamming weights, first defined by V.K. Wei as follows: Let C be an [n, k] linear code and D be a subcode. the support of D is the cardinality of the set of not-always-zero bit positions of D. the rth generalized Hamming weight of C, denoted by dr(C), is defined as the minimum support of r-dimensional subcode of C. the first generalized Hamming weight, d1(C) is just the minimum Hamming distance of the code C. It was shown that the generalized Hamming weight hierarchy of a linear code completely characterizes the performance of the code on the type II wire-tap channel defined by Ozarow and Wyner. In this paper, the second generalized Hamming weight of a double-error correcting BCH code and its dual code is derived. It is shown that d2(C) = 8 for all binary primitive double-error-correcting BCH codes. Also, we prove that the second generalized Hamming weight of [2m – 1, 2m]-dual BCH codes satisfies the Griesmer bound for m ≡ 1,2,3 (mod 4) and 0 (mod 12). © 1991, Springer Verlag. All rights reserved.

关键词： Hamming distance

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4th international symposium on applied algebra, algebraic algorithms and error-correcting codes, AAECC 1986

4th International Symposium on Applied Algebra, Algebraic Al...

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4th international symposium on applied algebra, algebraic algorithms and error-correcting codes, AAECC 1986

ISBN: (纸本)9783540192008

the proceedings contain 21 papers. the special focus in this conference is on applied algebra, algebraic algorithms and error-correcting codes. the topics include: Applicable algebra, error-correcting codes, combinatorics and computer algebra: An introduction to this volume;a symbolic manipulation system for combinatorial problems;standard bases and non-noetherianity: Non-commutative polynomial rings;embedding self-dual codes into projective space;the finite fourier-transform as a modular substitution;on computers and modular representations of SL (K);construction of SDMC codes over GF (2) or GF (3);fAST16: A software program for factorising polynomials over large GF(p);characterization of completely regular codes through p-polynomial association schemes;codes on hermitian curves;symmetries of cyclic extended goppa codes over F;from T(m) triangular graphs to single-error-correcting codes;some bounds for the construction of Gröbner bases;analysis of a class of algorithms for problems on trace languages;integration of graphical tools in a computer algebra system;type inference using unification in computer algebra;the weight distribution of double-error-correcting goppa codes;a simple analysis of the blokh-Zyablov decoding algorithm;design of a viterbi decoder with microprocessor-based serial implementation;on s-sum-sets (s odd) and three-weight projective codes;on the integration of numeric and algebraic computations.

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Applicable algebra, error-correcting codes, combinatorics and computer algebra: An introduction to this volume 4th

Applicable algebra, error-correcting codes, combinatorics an...

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4th international symposium on applied algebra, algebraic algorithms and error-correcting codes, AAECC 1986

作者： Beth, thomas

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the weight distribution of double-error-correcting goppa codes 4th

The weight distribution of double-error-correcting goppa cod...

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4th international symposium on applied algebra, algebraic algorithms and error-correcting codes, AAECC 1986

作者： Dür, Arne Institut für Mathematik Universität Innsbruck Techniker-Straße 25 InnsbruckA-6020 Austria

ISBN: (纸本)9783540192008

In this paper the weight distribution of binary Goppa codes with location set GF (2m) and irreducible quadratic Goppa polynomial is studied. these codes are all equivalent and have parameters [2m, 2m–2m, 5]. An explicit formula for the number of codewords of weight 5 and 6 is derived. the weight distribution of the dual codes is related to the weight distribution of a reversible irreducible cyclic code of length 2m+1 and dimension 2m whose weights can be expressed in terms of Kloosterman sums over GF (2m). As numerical examples the weight distribution of the double-error-correcting Goppa codes of block length 8,16,32, and 64 are computed. © 1988, Springer-Verlag.

关键词： codes (symbols)

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From T(m) triangular graphs to single-error-correcting codes 4th

From T(m) triangular graphs to single-error-correcting codes

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4th international symposium on applied algebra, algebraic algorithms and error-correcting codes, AAECC 1986

作者： Basart, J.M. Huguet, L. Dpt. d'Informàtica Fac. de Ciències Univ. Autònoma de Barcelona Bellaterra CataloniaOB193 Spain

ISBN: (纸本)9783540192008

We present a way to construct an infinite family of linear codes, with d=3, from a particular type of strongly regular graph. Using the incidence matrix and taking a tree of any nondirected and connected graph G(V,E) we can obtain the matrix of fundamental circuits and the one for fundamental cuts. these are respectively the generator and parity check matrices of a linear code. We are interested in the construction of triangular strongly regular graphs, named T(m). From T(m) and some results on the girth and the valency of a strongly regular graph G, for any integer m≥4, we obtain a linear code C(T(m)) with parameters: n=(m(m−1)(m−2))/2, k=(m(m−1)(m−3)+2)/2, d=3 and A1=An−1, A1 being the number of codewords of weight i in the code. Moreover we give some properties of its codewords set and its orthogonal one. Finally, an alternative method using lattice graphs Lz is proposed. © 1988, Springer-Verlag.

关键词： Matrix algebra

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applied algebra, algebraic algorithms and error-correcting codes 1

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丛书名： Lecture Notes in Computer Science

1000年

作者： Maria Bras-Amorós Tom Høholdt

ISBN: (数字)9783642021817

ISBN: (纸本)9783642021800

this book constitutes the refereed proceedings of the 18th international symposium on applied algebra, algebraic algorithms and error-correcting codes, AAECC-18, held in Tarragona, Spain, in June 2009. the 22 revised full papers presented together with 7 extended absstracts were carefully reviewed and selected from 50 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.

关键词： Coding and Information theory Cryptology Discrete Mathematics in Computer Science Symbolic and algebraic Manipulation Data Structures and Information theory algorithms

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applied algebra, algebraic algorithms and error-correcting codes 1

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丛书名： Lecture Notes in Computer Science

1000年

ISBN: (数字)9783540691938

ISBN: (纸本)9783540631637

this book constitutes the strictly refereed proceedings of the 12th international symposium on applied algebra, algebraic algorithms and error-correcting codes, AAECC-12, held in Toulouse, France, June 1997.;the 27 revised full papers presented were carefully selected by the program committee for inclusion in the volume. the papers address a broad range of current issues in coding theory and computer algebra spanning polynomials, factorization, commutative algebra, real geometry, group theory, etc. on the mathematical side as well as software systems, telecommunication, complexity theory, compression, signal processing, etc. on the computer science and engineering side.

关键词： theory of Computation algebra Applications of Mathematics Coding and Information theory Symbolic and algebraic Manipulation Numeric Computing

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