Automorphism groups of Grassmann codes
Copyright policy )Automorphism groups of Grassmann codes
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
FOS: Computer and information sciences, Computer Science - Information Theory, Spaces, Automorphism Group, automorphism group, Grassmannians, Schubert varieties, flag manifolds, Grassmann variety, Equivalence, Mathematics - Algebraic Geometry, Schubert divisor, 14M15, 20B25, 94B05, 94B27, Grassmann Variety, FOS: Mathematics, linear code, Affine Grassmann Code, Algebraic Geometry (math.AG), Linear codes (general theory), Information Theory (cs.IT), Finite automorphism groups of algebraic, geometric, or combinatorial structures, Grassmann code, affine Grassmann code, Schubert Divisor, Linear Code, Grassmann Code, Geometric methods (including applications of algebraic geometry) applied to coding theory
FOS: Computer and information sciences, Computer Science - Information Theory, Spaces, Automorphism Group, automorphism group, Grassmannians, Schubert varieties, flag manifolds, Grassmann variety, Equivalence, Mathematics - Algebraic Geometry, Schubert divisor, 14M15, 20B25, 94B05, 94B27, Grassmann Variety, FOS: Mathematics, linear code, Affine Grassmann Code, Algebraic Geometry (math.AG), Linear codes (general theory), Information Theory (cs.IT), Finite automorphism groups of algebraic, geometric, or combinatorial structures, Grassmann code, affine Grassmann code, Schubert Divisor, Linear Code, Grassmann Code, Geometric methods (including applications of algebraic geometry) applied to coding theory
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