Automorphism groups of Grassmann codes
arXiv:1204.5547 · doi:10.1016/j.ffa.2013.04.005
Abstract
We use a theorem of Chow (1949) on line-preserving bijections of Grassmannians to determine the automorphism group of Grassmann codes. Further, we analyze the automorphisms of the big cell of a Grassmannian and then use it to settle an open question of Beelen et al. (2010) concerning the permutation automorphism groups of affine Grassmann codes. Finally, we prove an analogue of Chow's theorem for the case of Schubert divisors in Grassmannians and then use it to determine the automorphism group of linear codes associated to such Schubert divisors. In the course of this work, we also give an alternative short proof of MacWilliams theorem concerning the equivalence of linear codes and a characterization of maximal linear subspaces of Schubert divisors in Grassmannians.
revised version
References in corpus (3)
Cited by in corpus (10)
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- A note on the automorphism group of Schubert varieties
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- An asymptotic formula in q for the number of [n,k] q-ary MDS codes