a BAPS is a binary sequence of length $n$ with an almost perfect autocorrelation: $$ A(\tau)=\left\{\begin{matrix} n & \tau=0 \\ k & \tau= {n \over 2} \\ 0 & else \end{matrix}\right. $$ for sequence of $\{ +1,-1\}^n$.
now, it is clear that $n$ is an even number, but why is $n\ mod\ 4 = 0$?