p-adic field as a vector space?

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Hello! Is there an equivalent of absolute(or relative)_vector_space for p-adic fields? I couldn't find anything! If not, is there any other way to realize a p-adic field extension as a vector space (over Q, but even over Q_p)? I'm trying to use linear_dependence in particular. Actually my main goal is to do something like what algdep does, but that command only seem to work for Q_p and not any extension!

I apologize for being an absolute illiterate with computers which shall show itself sooner or later!