Balanced and Almost Balanced Binary Sequences of Period pm - 1 with Optimal Autocorrelation Using the Polynomial

In this paper, we present a construction for binary sequences {s(t)} of period N = p" - 1 for an odd prime p based on the polynomial (z + l)d + azd + b with optimal three-level autocorrelation. I. CONSTRUCTION OF NEW BINARY SEQUENCES Recently, there has been a big progress in constructing bal- anced binary sequences of period 2" - l with ideal autocor- relation (l, 2, 41. The idea of the (new) construction is to use a special polynomial over finite fields. In this paper, we gen- eralize it to generate binary sequences of period pm - 1 with optimal autocorrelation for any prime p and an integer m. Let F denote the field of p" elements and F' = F\{O}. For a, b E F and a positive integer d, consider the subset of F' given by