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29 March 2024
 
  » arxiv » 1204.5547

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Automorphism groups of Grassmann codes
Sudhir R. Ghorpade ; Krishna V. Kaipa ;
Date 25 Apr 2012
AbstractWe determine the automorphism group of three families of linear codes associated with the Grassmann variety $G(ell,m)$ of $ell$ dimensional subspaces of $F_q^m$: 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 $G(ell,m) subset P^{inom{m}{ell}-1}$. 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 $Omega$.
Source arXiv, 1204.5547
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