All One Polynomial

An all one polynomial (AOP) is a polynomial used in finite fields, specifically GF(2) (binary). The AOP is a 1-equally spaced polynomial.

An AOP of degree m has all terms from xm to x0 with coefficients of 1, and can be written as

or

or

thus the roots of the all one polynomial of degree m are all (m+1)th roots of unity other than unity itself.