On finite pseudorandom binary sequences I: Measure of pseudorandomness, the Legendre symbol
Christian Mauduit ; András Sárközy
Acta Arithmetica, Tome 80 (1997), p. 365-377 / Harvested from The Polish Digital Mathematics Library
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     author = {Christian Mauduit and Andr\'as S\'ark\"ozy},
     title = {On finite pseudorandom binary sequences I: Measure of pseudorandomness, the Legendre symbol},
     journal = {Acta Arithmetica},
     volume = {80},
     year = {1997},
     pages = {365-377},
     zbl = {0886.11048},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav82i4p365bwm}
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Christian Mauduit; András Sárközy. On finite pseudorandom binary sequences I: Measure of pseudorandomness, the Legendre symbol. Acta Arithmetica, Tome 80 (1997) pp. 365-377. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav82i4p365bwm/

[000] [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. | Zbl 0859.94026

[001] [B-L] A. Barg and S. N. Lytsin, DC-constrained codes from Hadamard matrices, IEEE Trans. Inform. Theory 37 (1991), 801-807. | Zbl 0729.94009

[002] [C] J. W. S. Cassels, On a paper of Niven and Zuckerman, Pacific J. Math. 2 (1952), 555-557. | Zbl 0047.04402

[003] [C-T] F. R. K. Chung and P. Tetali, Communication complexity and quasirandomness, SIAM J. Discrete Math. 6 (1993), 110-123. | Zbl 0771.05073

[004] [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. | Zbl 0701.65008

[005] [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. | Zbl 0762.65001

[006] [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. | Zbl 0785.11043

[007] [EH-N3] J. Eichenauer-Herrmann and H. Niederreiter, Bounds for exponential sums and their applications to pseudorandom numbers, Acta Arith. 67 (1994), 269-281. | Zbl 0957.11050

[008] [F-I] J. Friedlander and H. Iwaniec, preprint.

[009] [F-M1] E. Fouvry et C. Mauduit, Sommes des chiffres et nombres presque premiers, Math. Ann. 305 (1996), 571-599.

[010] [F-M2] E. Fouvry et C. Mauduit, Méthodes de crible et fonctions sommes des chiffres, Acta Arith. 77 (1996), 339-351.

[011] [Ge] A. O. Gelfond, Sur les nombres qui ont des propriétés additives et multiplicatives données, Acta Arith. 13 (1968), 259-265. | Zbl 0155.09003

[012] [Iw] H. Iwaniec, Fourier coefficients of modular forms of half-integral weight, Invent. Math. 87 (1987), 385-401. | Zbl 0606.10017

[013] [Kn] D. E. Knuth, The Art of Computer Programming, Vol. 2, 2nd ed., Addison-Wesley, Reading, Mass., 1981.

[014] [Ko] A. N. Kolmogorov, On table of random numbers, Sankhyā A 25 (1963), 369-376. | Zbl 0126.33203

[015] [MW-S] F. J. MacWilliams and N. J. A. Sloane, Pseudo-random sequences and arrays, Proc. IEEE 64 (1976), 1715-1729.

[016] [ML] P. Martin-Löf, The definition of random sequences, Inform. and Control (Shenyang) 6 (1966), 602-619. | Zbl 0244.62008

[017] [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. | Zbl 0868.11004

[018] [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. | Zbl 0887.11008

[019] [Ni1] H. Niederreiter, Recent trends in random number and random vector generation, Ann. Oper. Res. 31 (1991), 323-345. | Zbl 0737.65001

[020] [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. | Zbl 0849.11055

[021] [Ni3] H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, SIAM, Philadelphia, 1992.

[022] [N-Z] I. Niven and H. S. Zuckerman, On the definition of normal numbers, Pacific J. Math. 1 (1951), 103-109. | Zbl 0042.26902

[023] [Sch] W. Schmidt, Equations over Finite Fields. An Elementary Approach, Lecture Notes in Math. 536, Springer, New York, 1976. | Zbl 0329.12001

[024] [Vin] I. M. Vinogradov, Elements of Number Theory, Dover, 1954.

[025] [We] A. Weil, Sur les courbes algébriques et les variétés qui s'en déduisent, Act. Sci. Ind. 1041, Hermann, Paris, 1948. | Zbl 0036.16001