• Corpus ID: 239016877

Affine Hermitian Grassmann Codes

  title={Affine Hermitian Grassmann Codes},
  author={Fernando Pi{\~n}ero-Gonz{\'a}lez and Doel Rivera Laboy},
The Grassmannian is an important object in Algebraic Geometry. One of the many techniques used to study the Grassmannian is to build a vector space from its points in the projective embedding and study the properties of the resulting linear code. We introduce a new class of linear codes, called Affine Hermitian Grassman Codes. These codes are the linear codes resulting from an affine part of the projection of the Polar Hermitian Grassmann codes. They combine Polar Hermitian Grassmann codes and… 


Line Hermitian Grassmann Codes and their Parameters
The structure of dual Grassmann codes
It is shown that the increase of value of successive generalized Hamming weights of a dual Grassmann code is 1 or 2, and the minimum weight codewords of the dual affine Grassmann codes are classified.
Affine Grassmann Codes
It is shown that affine Grassmann codes have a large automorphism group and the number of minimum weight codewords is determined and the length, dimension, and the minimum distance are determined.
A pr 2 01 8 Minimum distance of Orthogonal Line-Grassmann Codes in even characteristic
It is shown that for q even all minimum weight codewords are equivalent and that symplectic line-Grassmann codes are proper subcodes of codimension 2n of the orthogonal ones.
Minimum distance of Symplectic Grassmann codes
Line polar Grassmann codes of orthogonal type
Codes and caps from orthogonal Grassmannians
Duals of Affine Grassmann Codes and Their Relatives
It is proved that affine Grassmann codes and their duals have the property that they are linear codes generated by their minimum-weight codewords, which provides a clean analogue of a corresponding result for generalized Reed-Muller codes.
Ghorpade , and Tom Høholdt . Duals of affine Grassmann codes and their relatives
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