Linear complexity of modified Jacobi sequences

Legendre sequences are a well-known class of binary sequences, which possess good periodic and aperiodic autocorrelation functions. They are also known to exhibit high linear complexity, which makes them significant for cryptographic applications. Jacobi and modified Jacobi sequences are constructed by combining two appropriate Legendre sequences and they also have good correlation properties. This class also contains the Twin Prime sequences as a special case. The authors report the results of subjecting a wide range of modified Jacobi sequences to the Berlekamp-Massey algorithm in order to establish their linear complexities. The results obtained confirm that some members of this class also have high linear complexity. The findings display sufficient structure to enable the general form of the linear complexity and the corresponding generator polynomials to be conjectured