Generation of further pseudorandom binary sequences, I (Blowing up a single sequence)

Christian Mauduit (1) , Katalin Gyarmati (2, 3) , András Sárközy (3)

1 I2M - Institut de Mathématiques de Marseille
2 MTA - Hungarian Academy of Sciences
3 Department of Algebra and Number Theory [Budapest]

Assume that a binary sequence is given with strong pseudorandom properties. An algorithm is presented and studied which prepares many further binary sequences from the given one. It is shown that if certain conditions hold then each of the sequences obtained in this way also possesses strong pseudorandom properties. Moreover, it is proved that certain large families of these sequences also posses strong pseudorandom properties.

Mots clés: pseudorandom; families of binary sequences; well-distribution; correlation; family complexity

Domaines: Théorie des nombres [math.NT]

Christian Mauduit, Katalin Gyarmati, András Sárközy. Generation of further pseudorandom binary sequences, I (Blowing up a single sequence). Uniform Distribution Theory, 2015, 10 (1), pp.35-61. ⟨hal-01272742⟩