Construction of cyclic extensions of degree $p^2$ for a complete field

In the present paper we embed a given cyclic extension of degree $p$ of a complete discrete valuation field of characteristic 0 with an arbitrary residue field of characteristic $p>0$ into a cyclic extension of degree $p^2$. The result extends the construction obtained by S. V. Vostokov and I. B. Zhukov in terms of Witt vectors, to a wider interval of values for the ramification jump of the original field extension.