Families of sequences with good family complexity and cross-correlation measure

arXiv:2004.13938v3 Announce Type: replace-cross
Abstract: In this paper we study pseudorandomness of a family of sequences in terms of two measures, the family complexity ($f$-complexity) and the cross-correlation measure of order $\ell$. We consider sequences not only on binary alphabet but also on $k$-symbols ($k$-ary) alphabet. We first generalize some known methods on construction of the family of binary pseudorandom sequences. We prove a bound on the $f$-complexity of a large family of binary sequences of Legendre-symbols of certain irreducible …

alphabet arxiv binary complexity correlation cs.cr cs.it families family good math.it math.nt measure order study terms