A construction of binary sequences with period $4N$ and optimal autocorrelation magnitude has been investigated based on sampling and interleaving technique. We determine the exact value of the linear complexity of the constructed sequences according to the deep relationship among the characteristic polynomials, and show it is $2N+2$. Moreover, we determine the 2-adic complexity of these sequences by the autocorrelation function, and show it can attain the maximum value. Results show that such sequences can resist both the Berlekamp-Massey attack and the Rational Approximation Algorithm, in addition are good for communication.