New Integer Valued Sequences with 2-Level Autocorrelation Constructed from DHT New Ternary and Quaternary Sequences with 2-Level Autocorrelation

p, a prime; n, a positive integer; q = pn. f (x), a polynomial function from Fq to Fp. Tr(x) = x + xp + · · ·+ xpn−1, the trace function from Fq to Fp. α, a primitive element in Fq. A sequence a = {ai} where ai = f (αi), i = 0,1, · · · , is a sequence over Fp with period q − 1 or dividing q − 1. If f (x) = Tr(x t) where (t,q − 1) = 1, then a is an m-sequence over Fp, i.e., m-sequence ← → Tr(x t)