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Automorphism groups of Grassmann codes | Sudhir R. Ghorpade
; Krishna V. Kaipa
; | Date: |
25 Apr 2012 | Abstract: | We 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 | Services: | Forum | Review | PDF | Favorites |
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