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An $(r,M,2\delta;k)_q$ constant--dimension subspace code, $\delta >1$, is acollection $\cal C$ of $(k-1)$--dimensional projective subspaces of ${\rmPG(r-1,q)}$ such that every $(k-\delta)$--dimensional projective subspace of${\rm PG(r-1,q)}$ is contained in at most a member of $\cal C$.Constant--dimension subspace codes gained recently lot of interest due to thework by Koetter and Kschischang, where they presented an application of suchcodes for error-correction in random network coding. Here a $(2n,M,4;n)_q$constant--dimension subspace code is constructed, for every $n \ge 4$. The sizeof our codes is considerably larger than all known constructions so far,whenever $n > 4$. When $n=4$ a further improvement is provided by constructingan $(8,M,4;4)_q$ constant--dimension subspace code, with $M =q^{12}+q^2(q^2+1)^2(q^2+q+1)+1$.

Subspace codes in PG(2n-1,q)