A Binary Sequence Generated by Legendre Symbol and Primitive Polynomial over Odd Characteristic

摘要

Let p he an odd characteristic and m be the degree of primitive polynomial f(x). Let ω be its zero, that is a primitive element in F~*_(p~m), then the sequence S - {s_i}, Si = Tr (ω~i), i = 0,1,2, …becomes a maximum length sequence, where Tr (·) is the trace function over F_p. On this fact, this paper proposes to binarize the sequence by using Legendre symbol. Then, it is shown that the obtained binary sequence has the period L = 2(p~m - l)/(p - 1) and a certain periodic autocorrelation. This paper also shows a small example.