Low-Correlation, High-Nonlinearity Sequences for Multiple-Code CDMA

Families of binary low-correlation sequences with high nonlinearity (in relation with their Walsh Hadamard transform) are constructed by using the most significant bit of linear recurrence sequences over the ring Zopf₂ ^l, for lges3. The engineering motivation is the design of a multiple-code code-division multiple-access (CDMA) scheme with a control of low peak-to-average power ratio (PAPR). Proof techniques combine Galois ring theory (local Weil bound) with spectral analysis over the additive group of Zopf₂ ^l. New estimates on the size of weighted degree trace codes are derived. The parameters of the sequences families constructed are shown to lie above a modified Varshamov-Gilbert bound