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1997 | 82 | 4 | 365-377
Tytuł artykułu

On finite pseudorandom binary sequences I: Measure of pseudorandomness, the Legendre symbol

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Czasopismo
Rocznik
Tom
82
Numer
4
Strony
365-377
Opis fizyczny
Daty
wydano
1997
otrzymano
1997-02-04
Twórcy
  • Institut de Mathématiques de Luminy, CNRS-UPR 9016, 163 av. de Luminy, Case 930, F-13288 Marseille Cédex 9, France
  • Department of Algebra and Number Theory, Eötvös Loránd University, Muzeum krt. 6-8, H-1088 Budapest, Hungary
Bibliografia
  • [B] A. Barg, Exponential sums and constrained error-correcting codes, in: Algebraic Coding (Paris, 1991), Lecture Notes in Comput. Sci. 573, Springer, 1992, 16-22.
  • [B-L] A. Barg and S. N. Lytsin, DC-constrained codes from Hadamard matrices, IEEE Trans. Inform. Theory 37 (1991), 801-807.
  • [C] J. W. S. Cassels, On a paper of Niven and Zuckerman, Pacific J. Math. 2 (1952), 555-557.
  • [C-T] F. R. K. Chung and P. Tetali, Communication complexity and quasirandomness, SIAM J. Discrete Math. 6 (1993), 110-123.
  • [E-L-T] J. Eichenauer, J. Lehn and A. Topuzoğlu, A nonlinear congruential pseudorandom generator with power of two modulus, Math. Comp. 51 (1988), 757-759.
  • [EH-N1] J. Eichenauer-Herrmann and H. Niederreiter, Lower bounds for the discrepancy of inversive congruential pseudorandom numbers with power of two modulus, Math. Comp. 58 (1992), 775-779.
  • [EH-N2] J. Eichenauer-Herrmann and H. Niederreiter, Kloosterman-type sums and the discrepancy of nonoverlapping pairs of inversive congruential pseudorandom numbers, Acta Arith. 65 (1993), 185-194.
  • [EH-N3] J. Eichenauer-Herrmann and H. Niederreiter, Bounds for exponential sums and their applications to pseudorandom numbers, Acta Arith. 67 (1994), 269-281.
  • [F-I] J. Friedlander and H. Iwaniec, preprint.
  • [F-M1] E. Fouvry et C. Mauduit, Sommes des chiffres et nombres presque premiers, Math. Ann. 305 (1996), 571-599.
  • [F-M2] E. Fouvry et C. Mauduit, Méthodes de crible et fonctions sommes des chiffres, Acta Arith. 77 (1996), 339-351.
  • [Ge] A. O. Gelfond, Sur les nombres qui ont des propriétés additives et multiplicatives données, Acta Arith. 13 (1968), 259-265.
  • [Iw] H. Iwaniec, Fourier coefficients of modular forms of half-integral weight, Invent. Math. 87 (1987), 385-401.
  • [Kn] D. E. Knuth, The Art of Computer Programming, Vol. 2, 2nd ed., Addison-Wesley, Reading, Mass., 1981.
  • [Ko] A. N. Kolmogorov, On table of random numbers, Sankhyā A 25 (1963), 369-376.
  • [MW-S] F. J. MacWilliams and N. J. A. Sloane, Pseudo-random sequences and arrays, Proc. IEEE 64 (1976), 1715-1729.
  • [ML] P. Martin-Löf, The definition of random sequences, Inform. and Control (Shenyang) 6 (1966), 602-619.
  • [M-S1] C. Mauduit and A. Sárközy, On the arithmetic structure of sets characterized by sum of digits properties, J. Number Theory 61 (1996), 25-38.
  • [M-S2] C. Mauduit and A. Sárközy, On the arithmetic structure of the integers whose sum of digits is fixed, Acta Arith. 81 (1997), 145-173.
  • [Ni1] H. Niederreiter, Recent trends in random number and random vector generation, Ann. Oper. Res. 31 (1991), 323-345.
  • [Ni2] H. Niederreiter, New methods for pseudorandom number and pseudorandom vector generation, in: Proc. 1992 Winter Simulation Conference, J. J. Swain et al. (eds.), IEEE Press, Piscataway, N.J., 1992, 264-269.
  • [Ni3] H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, SIAM, Philadelphia, 1992.
  • [N-Z] I. Niven and H. S. Zuckerman, On the definition of normal numbers, Pacific J. Math. 1 (1951), 103-109.
  • [Sch] W. Schmidt, Equations over Finite Fields. An Elementary Approach, Lecture Notes in Math. 536, Springer, New York, 1976.
  • [Vin] I. M. Vinogradov, Elements of Number Theory, Dover, 1954.
  • [We] A. Weil, Sur les courbes algébriques et les variétés qui s'en déduisent, Act. Sci. Ind. 1041, Hermann, Paris, 1948.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-aav82i4p365bwm
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