The constructions of almost binary sequence pairs with three-level correlation based on cyclotomy

In this paper, a new class of almost binary sequence pair with a single zero element is presented. The almost binary sequence pairs with three-level correlation are constructed based on cyclotomic numbers of order 2, 4, and 6. Most of them have good correlation and balance property, whose maximum nontrivial correlation magnitudes are 2 and the difference between the numbers of occurrence of +1’s and ′-1’s are 0 or 1. In addition, the corresponding binary sequence pairs are investigated as well and we can also get some kinds of binary sequence pairs with optimum balance and good correlation.