New sequences with zero autocorrelation (Q1812366)

The authors give a new construction method for unimodular delta-correlated sequences of length \(p\) (a prime). This method uses so-called Gauss periods. In the case \(p=3f+1\) it is shown that the elements are defined by roots of a polynomial of degree 12 over \(\mathbb{Z}\) (the integers) for one family and by roots of a polynomial of degree 6 for another family. For \(p=3,5,7\) and 13 the methods can be shown to generate all equivalence classes of unimodular delta-correlated sequences, where the equivalence is defined by a specific group of transformations. The authors conjecture that this is true for any prime \(p\).