Integrated Sidelobe Level of sets of Rotated Legendre Sequences

We here address the problem of constructing sets of sequences with low integrated aperiodic auto- and cross-correlations when the constraint of antipodal symbols is enforced. Our method is based on Legendre Sequences and on the correlation properties of their rotations. Starting from this idea, an extremely lightweight procedure driven by asymptotic considerations yields sets of antipodal sequences that largely outperform known sequence families or algorithms, actually positioning extremely close to the performance upper bound.