Abstract
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
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