Automorphism groups of Grassmann codes

Details Automorphism groups of Grassmann codes Automorphism groups of Grassmann codes

2012-04-25

arxiv.org/abs/1204.5547v1

Computer Science

Information Theory

Scientific paper

We determine the automorphism group of three families of linear codes associated with the Grassmann variety $G(\ell,m)$ of $\ell$ dimensional subspaces of $\bF_q^m$: The Grassmann codes $C(\ell,m)$, the Affine Grassmann codes $C^A(l,m)$, and the Schubert divisor codes $C_{\Omega}(\ell,m)$. The code $C(\ell,m)$ corresponds to the projective system defined by the Pl\"{u}cker embedding $G(\ell,m) \subset \bP^{\binom{m}{\ell}-1}$. The code $C^A(\ell,m)$ is obtained by puncturing $C(\ell,m)$ on the points of a codimension one Schubert variety $\Omega$ of $G(\ell,m)$, and the code $C_{\Omega}(\ell,m)$ is obtained by puncturing $C(\ell,m)$ on the complement of $\Omega$.

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