### Abstract

This paper studies links between uniform pseudorandom sequences of real numbers in [0, 1) and pseudorandom binary sequences. It is proved that good pseudorandom [0, 1) sequences induce binary sequences that have small correlation and well-distribution measures. On the other hand, given a binary sequence with small combined well-distribution-correlation measure, it is shown how to construct a [0, 1) sequence with small discrepancy. The special cases of linear congruential pseudorandom sequences and of Legendre symbol sequences are analyzed in more detail.

Original language | English |
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Pages (from-to) | 305-324 |

Number of pages | 20 |

Journal | Publicationes Mathematicae |

Volume | 71 |

Issue number | 3-4 |

Publication status | Published - Nov 22 2007 |

### Keywords

- Correlation measures
- Discrepancy
- Legendre symbol sequences
- Linear congruential method
- Pseudorandom binary sequences
- Uniform pseudorandom sequences

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Mauduit, C., Niederreiter, H., & Sarközy, A. (2007). On pseudorandom [0, 1 and binary sequences.

*Publicationes Mathematicae*,*71*(3-4), 305-324.