  We prove that if $n >k^2$ then a $k$-dimensional linear code of length $n$
over ${\mathbb F}_{q^2}$ has a truncation which is linearly equivalent to a
Hermitian self-orthogonal linear code. In the contrary case we prove that
truncations of linear codes to codes equivalent to Hermitian self-orthogonal
linear codes occur when the columns of a generator matrix of the code do not
impose independent conditions on the space of Hermitian forms. In the case that
there are more than $n$ common zeros to the set of Hermitian forms which are
zero on the columns of a generator matrix of the code, the additional zeros
give the extension of the code to a code that has a truncation which is
equivalent to a Hermitian self-orthogonal code.
