The Single Cycle T-functions

In this paper the single cycle T-functions are studied. Making use of the explicit formulas of sum and product of 2-adic integers, we present the necessary and sufficient conditions on the generalized polynomial p̃(x) = a0⊕a1x + ⊕ · · · + ⊕adx d(mod2n) being a single cycle T-function. Furthermore, for any given generalized polynomial, we can deduce some expressions about its coefficients by which we can determine whether it is single cycle or not.