\tau_p\,x_p\oplus\tau_p\,x_{2007-p}=\underbrace{000...000}_{2007-p}\underbrace{1...1}_p\oplus\underbrace{11...11}_{2007-2p}\underbrace{0...0}_p\underbrace{1...1}_p=\underbrace{11...11}_{2007-2p}\underbrace{00...00}_{2p}