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Binary periodic sequences with good autocorrelation property have manyapplications in many aspects of communication. In past decades many series ofsuch binary sequences have been constructed. In the application ofcryptography, such binary sequences are required to have larger linearcomplexity. Tang and Ding \cite{X. Tang} presented a method to construct aseries of binary sequences with period 4$n$ having optimal autocorrelation.Such sequences are interleaved by two arbitrary binary sequences with period$n\equiv 3\pmod 4$ and ideal autocorrelation. In this paper we present ageneral formula on the linear complexity of such interleaved sequences.Particularly, we show that the linear complexity of such sequences with period4$n$ is not bigger than $2n+2$. Interleaving by several types of known binarysequences with ideal autocorrelation ($m$-sequences, Legendre, twin-prime andHall's sequences), we present many series of such sequences having the maximumvalue $2n+2$ of linear complexity which gives an answer of a problem raised byN. Li and X. Tang \cite{N. Li}. Finally, in the conclusion section we show thatit can be seen easily that the 2-adic complexity of all such interleavedsequences reaches the maximum value $\log_{2}(2^{4n}-1)$.

Linear Complexity of Binary Interleaved Sequences of Period 4n