15 research outputs found
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.Comment: revised versio
Implementing Line-Hermitian Grassmann codes
In [I. Cardinali and L. Giuzzi. Line Hermitian Grassmann codes and their
parameters. Finite Fields Appl., 51: 407-432, 2018] we introduced line
Hermitian Grassmann codes and determined their parameters. The aim of this
paper is to present (in the spirit of [I. Cardinali and L. Giuzzi. Enumerative
coding for line polar Grassmannians with applications to codes. Finite Fields
Appl., 46:107-138, 2017]) an algorithm for the point enumerator of a line
Hermitian Grassmannian which can be usefully applied to get efficient encoders,
decoders and error correction algorithms for the aforementioned codes.Comment: 26 page
Line Polar Grassmann Codes of Orthogonal Type
Polar Grassmann codes of orthogonal type have been introduced in I. Cardinali
and L. Giuzzi, \emph{Codes and caps from orthogonal Grassmannians}, {Finite
Fields Appl.} {\bf 24} (2013), 148-169. They are subcodes of the Grassmann code
arising from the projective system defined by the Pl\"ucker embedding of a
polar Grassmannian of orthogonal type. In the present paper we fully determine
the minimum distance of line polar Grassmann Codes of orthogonal type for
odd
Line polar Grassmann codes of orthogonal type
Polar Grassmann codes of orthogonal type have been introduced in I. Cardinali and L. Giuzzi, \emph{Codes and caps from orthogonal Grassmannians}, {Finite Fields Appl.} {\bf 24} (2013), 148-169. They are subcodes of the Grassmann code arising from the projective system defined by the Pl\"ucker embedding of a polar Grassmannian of orthogonal type. In the present paper we fully determine the minimum distance of line polar Grassmann Codes of orthogonal type for q odd