On the gowers norm of pseudorandom binary sequences

Bulletin of the Australian Mathematical Society

Volumn 79, Issue 2, 2009, Pages 259-271

  Niederreiter, Harald ^a   Rivat, Joël ^b  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^b AIX MARSEILLE UNIVERSITÉ   (France)

Author keywords

additive character; binary sequence; correlation; Gowers norm; pseudorandom

Indexed keywords

EID: 70349641259     PISSN: 00049727     EISSN: 17551633     Source Type: Journal    
DOI: 10.1017/S0004972708001184     Document Type: Article

References (11)

1. L. Goubin, Ch. Mauduit and A. Sark̈ozy, Construction of large families of pseudorandom binary sequences, J. Number Theory 106 (2004), 56-69. (Pubitemid 38582661)
2. W. T. Gowers, A new proof of Szemerédi's theorem, Geom. Funct. Anal. 11 (2001), 465-588.
3. Ch. Mauduit, H. Niederreiter and A. Sark̈ozy, On pseudorandom [0, 1) and binary sequences, Publ. Math. Debrecen 71 (2007), 305-324.
4. Ch. Mauduit and A. Sark̈ozy, On finite pseudorandom binary sequences I: Measure of pseudorandomness, the Legendre symbol, Acta Arith. 82 (1997), 365-377. (Pubitemid 127340466)
5. C. J. Moreno and O. Moreno, Exponential sums and Goppa codes: I, Proc. Amer. Math. Soc. 111 (1991), 523-531.
6. H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods (SIAM, Philadelphia, PA, 1992).
7. H. Niederreiter and J. Rivat, On the correlation of pseudorandom numbers generated by inversive methods, Monatsh. Math. 153 (2008), 251-264.
8. H. Niederreiter, J. Rivat and A. Sark̈ozy, Pseudorandom sequences of binary vectors, Acta Arith. 133 (2008), 109-125.
9. H. Niederreiter and I. E. Shparlinski, Recent advances in the theory of nonlinear pseudorandom number generators, in: Monte Carlo and Quasi-Monte Carlo Methods 2000 (Springer, Berlin, 2000), pp. 86-102.
10. H. Niederreiter and A. Winterhof, Incomplete exponential sums over finite fields and their applications to new inversive pseudorandom number generators, Acta Arith. 93 (2000), 387-399.
11. On the structure of inversive pseudorandom number generators, in: AAECC 2007, Lecture Notes in Computer Science, 4851 (Springer, Berlin, 2007), pp. 208-216.