  The projective space $\mathbb{P}_q(n)$, i.e. the set of all subspaces of the
vector space $\mathbb{F}_q^n$, is a metric space endowed with the subspace
distance metric. Braun, Etzion and Vardy argued that codes in a projective
space are analogous to binary block codes in $\mathbb{F}_2^n$ using a framework
of lattices. They defined linear codes in $\mathbb{P}_q(n)$ by mimicking key
features of linear codes in the Hamming space $\mathbb{F}_2^n$. In this paper,
we prove that a linear code in a projective space forms a sublattice of the
corresponding projective lattice if and only if the code is closed under
intersection. The sublattice thus formed is geometric distributive. We also
present an application of this lattice-theoretic characterization.
