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Volumn 44, Issue 3, 2006, Pages 897-907

Numerical cubature using error-correcting codes

Author keywords

Cubature formulas; Error correcting codes; Orthogonal arrays

Indexed keywords

CUBATURE FORMULAS; EQUAL-WEIGHT PRODUCT FORMULAS; ERROR-CORRECTING CODES; ORTHOGONAL ARRAYS;

EID: 34547338443     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/040615572     Document Type: Article
Times cited : (18)

References (22)
  • 1
    • 50549175697 scopus 로고
    • On a class of error correcting binary group codes
    • R. C. BOSE AND D. K. RAY-CHAUDHURI, On a class of error correcting binary group codes, Information and Control, 3 (1960), pp. 68-79.
    • (1960) Information and Control , vol.3 , pp. 68-79
    • BOSE, R.C.1    RAY-CHAUDHURI, D.K.2
  • 2
    • 0037508476 scopus 로고    scopus 로고
    • A. R. CALDERBANK, R. H. HARDIN, E. M. RAINS, P. W. SHOR, AND N. J. A. SLOANE, A group-theoretic framework for the construction of packings in Grassmannian spaces, J. Algebraic Combin., 9 (1999), pp. 129-140, arXiv:math.CO/0208002.
    • A. R. CALDERBANK, R. H. HARDIN, E. M. RAINS, P. W. SHOR, AND N. J. A. SLOANE, A group-theoretic framework for the construction of packings in Grassmannian spaces, J. Algebraic Combin., 9 (1999), pp. 129-140, arXiv:math.CO/0208002.
  • 4
    • 0038054072 scopus 로고    scopus 로고
    • An encyclopaedia of cubature formulas
    • R. COOLS, An encyclopaedia of cubature formulas, J. Complexity, 19 (2003), pp. 445-453.
    • (2003) J. Complexity , vol.19 , pp. 445-453
    • COOLS, R.1
  • 6
    • 0007190882 scopus 로고
    • Invariant integration formulas for the n-simplex by combinatorial methods
    • A. GRUNDMANN AND H. M. MÖLLER, Invariant integration formulas for the n-simplex by combinatorial methods, SIAM J. Numer. Anal., 15 (1978), pp. 282-290.
    • (1978) SIAM J. Numer. Anal , vol.15 , pp. 282-290
    • GRUNDMANN, A.1    MÖLLER, H.M.2
  • 7
    • 34547377369 scopus 로고
    • Construction techniques for some thin sets in duals of compact abelian groups
    • D. HAJELA, Construction techniques for some thin sets in duals of compact abelian groups, Ann. Inst. Fourier (Grenoble), 36 (1986), pp. 137-166.
    • (1986) Ann. Inst. Fourier (Grenoble) , vol.36 , pp. 137-166
    • HAJELA, D.1
  • 8
    • 0028384429 scopus 로고    scopus 로고
    • 4-linearity of Kerdock, Preparata, Goethals, and related codes, IEEE Trans. Inform. Theory, 40 (1994), pp. 301-319, arXiv:math.CO/0207208.
    • 4-linearity of Kerdock, Preparata, Goethals, and related codes, IEEE Trans. Inform. Theory, 40 (1994), pp. 301-319, arXiv:math.CO/0207208.
  • 10
    • 0000292532 scopus 로고
    • Codes correcteurs d'erreurs
    • A. HOCQUENGHEM, Codes correcteurs d'erreurs, Chiffres, 2 (1959), pp. 147-156.
    • (1959) Chiffres , vol.2 , pp. 147-156
    • HOCQUENGHEM, A.1
  • 11
    • 0038257908 scopus 로고
    • A class of low-rate nonlinear binary codes
    • A. M. KERDOCK, A class of low-rate nonlinear binary codes, Information and Control, 20 (1972), pp. 182-187.
    • (1972) Information and Control , vol.20 , pp. 182-187
    • KERDOCK, A.M.1
  • 12
    • 84858107098 scopus 로고    scopus 로고
    • Advances in Multivariate Approximation Witten-Bommerholz, Math. Res. 107, Wiley-VCH, Berlin
    • H. KÖNIG, Cubature formulas on spheres, in Advances in Multivariate Approximation (Witten-Bommerholz, 1998), Math. Res. 107, Wiley-VCH, Berlin, 1999, pp. 201-211.
    • (1998) Cubature formulas on spheres , pp. 201-211
    • KÖNIG, H.1
  • 13
    • 15844405074 scopus 로고    scopus 로고
    • G. KUPERBERG, Special moments, Adv. in Appl. Math., 34 (2005), pp. 853-870, arXiv:math.PR/0408360.
    • G. KUPERBERG, Special moments, Adv. in Appl. Math., 34 (2005), pp. 853-870, arXiv:math.PR/0408360.
  • 14
    • 34547375315 scopus 로고    scopus 로고
    • F. J. MACWLLLIAMS AND N. J. A. SLOANE, The Theory of Error-Correcting Codes, North-Holland Math. Library 16, North-Holland, Amsterdam, 1977.
    • F. J. MACWLLLIAMS AND N. J. A. SLOANE, The Theory of Error-Correcting Codes, North-Holland Math. Library 16, North-Holland, Amsterdam, 1977.
  • 15
    • 8344289793 scopus 로고
    • Point sets and sequences with small discrepancy
    • H. NIEDERREITER, Point sets and sequences with small discrepancy, Monatsh. Math., 104 (1987), pp. 273-337.
    • (1987) Monatsh. Math , vol.104 , pp. 273-337
    • NIEDERREITER, H.1
  • 16
    • 0033238933 scopus 로고    scopus 로고
    • Simple cubature formulas with high polynomial exactness
    • E. NOVAK AND K. RITTER, Simple cubature formulas with high polynomial exactness, Constr. Approx., 15 (1999), pp. 499-522.
    • (1999) Constr. Approx , vol.15 , pp. 499-522
    • NOVAK, E.1    RITTER, K.2
  • 17
    • 0037416995 scopus 로고    scopus 로고
    • A comparison between (quasi-)Monte Carlo and cubature rule based methods for solving high-dimensional integration problems
    • R. SCHÜRER, A comparison between (quasi-)Monte Carlo and cubature rule based methods for solving high-dimensional integration problems, Math. Comput. Simulation, 62 (2003), pp. 509-517.
    • (2003) Math. Comput. Simulation , vol.62 , pp. 509-517
    • SCHÜRER, R.1
  • 18
    • 48549108193 scopus 로고
    • Averaging sets: A generalization of mean values and spherical designs
    • P. D. SEYMOUR AND T. ZASLAVSKY, Averaging sets: A generalization of mean values and spherical designs, Adv. in Math., 52 (1984), pp. 213-240.
    • (1984) Adv. in Math , vol.52 , pp. 213-240
    • SEYMOUR, P.D.1    ZASLAVSKY, T.2
  • 19
    • 0005075358 scopus 로고    scopus 로고
    • n-dimensional Euclidean space
    • n-dimensional Euclidean space, J. Algebraic Cornbin., 10 (1999), pp. 279-288.
    • (1999) J. Algebraic Cornbin , vol.10 , pp. 279-288
    • SIDELNIKOV, V.M.1
  • 20
    • 0003769405 scopus 로고
    • Approximate Calculation of Multiple Integrals
    • Prentice-Hall, Englewood Cliffs, NJ
    • A. H. STROUD, Approximate Calculation of Multiple Integrals, Prentice-Hall Series in Automatic Computation, Prentice-Hall, Englewood Cliffs, NJ, 1971.
    • (1971) Prentice-Hall Series in Automatic Computation
    • STROUD, A.H.1
  • 21
    • 1542771653 scopus 로고    scopus 로고
    • Asymmetric cubature formulae with few points in high dimension for symmetric measures
    • N. VLCTOIR, Asymmetric cubature formulae with few points in high dimension for symmetric measures, SIAM J. Numer. Anal., 42 (2004), pp. 209-227.
    • (2004) SIAM J. Numer. Anal , vol.42 , pp. 209-227
    • VLCTOIR, N.1
  • 22
    • 84858096425 scopus 로고    scopus 로고
    • MAGMA, http://magma.maths.usyd.edu.au/.
    • MAGMA


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.