The number of invariant subspaces under a linear operator on finite vector spaces

Harald Fripertinger

doi:10.3934/amc.2011.5.407

Article Contents

2011, Volume 5, Issue 2: 407-416. Doi: 10.3934/amc.2011.5.407

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The number of invariant subspaces under a linear operator on finite vector spaces

Harald Fripertinger^1,

1.
Institut für Mathematik, Karl-Franzens Universität Graz, Heinrichstr. 36/4, A-8010 Graz

Received: February 28, 2010

Revised: March 31, 2011

Published: April 2011

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Abstract

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.

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Mathematics Subject Classification: Primary: 05E18; Secondary: 47A46.

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