Large families of sequences with near-optimal correlations and large linear span

In order to build spread-spectrum communication systems based on the CDMA paradigm, it is necessary to have large families of binary sequences with low pairwise correlation values. For these systems to have resistance to certain cryptanalytic attacks and resistance to jamming, the sequences must have large linear span. We describe certain families of sequences that have these desirable properties. The sequences are based on families of quadratic forms over finite fields.