The number of invariant subspaces under a linear operator on finite vector spaces
Harald Fripertinger
Advances in Mathematics of Communications 2011, 5(2): 407-416 doi: 10.3934/amc.2011.5.407
Let $V$ be an $n$-dimensional vector space over the finite field $\mathbb F$q and $T$ a linear operator on $V$. For each $k\in\{1,\ldots,n\}$ we determine the number of $k$-dimensional $T$-invariant subspaces of $V$. Finally, this method is applied for the enumeration of all monomially nonisometric linear $(n,k)$-codes over $\mathbb F$q.
keywords: cyclic vector space monomially nonisometric linear codes. enumeration nite eld Invariant subspaces nite vector space

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