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In 2008, a class of binary sequences of period $N=4(2^k-1)(2^k+1)$ withoptimal autocorrelation magnitude has been presented by Yu and Gong based on an$m$-sequence, the perfect sequence $(0,1,1,1)$ of period $4$ and interleavingtechnique. In this paper, we study the 2-adic complexities of these sequences.Our results show that they are larger than $N-2\lceil\mathrm{log}_2N\rceil+4 $(which is far larger than $N/2$) and could attain the maximum value $N$ ifsuitable parameters are chosen, i.e., the 2-adic complexity of this class ofinterleaved sequences is large enough to resist the Rational ApproximationAlgorithm.

The 2-adic complexity of Yu-Gong sequences with interleaved structure and optimal autocorrelation magnitude