A New Family of Binary Sequences Based on the Generalized ERC Construction

Families of binary sequences with good auto- or cross-correlation properties are required in areas such as cryptography, wireless communications, and digital watermarking. Algebraic constructions present an advantage over random sequences in that fixed bounds can be provided for the off-peak correlation. The interleave and the composition method take a well-distributed pseudonoise sequence, such as an m-sequence, that can be extended to produce larger families with given properties and longer periods. The interleave method or row-by-row folding of a sequence is a popular approach to generate families such as Gordon Mill Welch (GMW) sequences, which are constructed using a shift sequence with good correlation properties. The method of composition (a different approach) also requires a shift sequence and a pseudonoise sequence to construct a new family more related with multidimensional periodic arrays. In this work, we develop new families of binary sequences with good pseudorandom properties based on both the interleave and composition methods, which offer flexible periods and easy implementation. This new construction is based on the generalized Extended Rational Cycle (ERC) construction developed by Rivat and Niederreiter. The results show that for certain parameters the obtained families are close to optimal in terms of family size and correlation.