A Family of Binary Sequences from Interleaved Construction and their Cryptographic Properties

Families of pseudorandom sequences with low cross correlation have important applications in communications and cryptography. Among several known constructions of sequences with low cross correlations, interleaved constructions proposed by Gong uses two sequences of the same period with two-level autocorrelation. In this paper, we study the balance property and the cross correlation of interleaved sequences such that the base sequences may not have the same period, or they may not have two-level autocorrelation. In particular, we study the interleaved sequences of two Legendre sequences of periods p and q, respectively, where p and q are odd prime numbers.