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In cryptography, we hope a sequence over $\mathbb{Z}_m$ with period $N$having larger $m$-adic complexity. Compared with the binary case, thecomputation of 4-adic complexity of knowing quaternary sequences has not beenwell developed. In this paper, we determine the 4-adic complexity of thequaternary cyclotomic sequences with period 2$p$ defined in [6]. The mainmethod we utilized is a quadratic Gauss sum $G_{p}$ valued in$\mathbb{Z}_{4^N-1}$ which can be seen as a version of classical quadraticGauss sum. Our results show that the 4-adic complexity of this class ofquaternary cyclotomic sequences reaches the maximum if $5\nmid p-2$ and closeto the maximum otherwise.

The 4-Adic Complexity of A Class of Quaternary Cyclotomic Sequences with Period 2p