Decomposable subspaces, linear sections of Grassmann varieties, and higher weights of Grassmann codes
نویسندگان
چکیده
منابع مشابه
Decomposable subspaces, linear sections of Grassmann varieties, and higher weights of Grassmann codes
Given a homogeneous component of an exterior algebra, we characterize those subspaces in which every nonzero element is decomposable. In geometric terms, this corresponds to characterizing the projective linear subvarieties of the Grassmann variety with its Plücker embedding. When the base field is finite, we consider the more general question of determining the maximum number of points on sect...
متن کاملHigher Weights of Grassmann Codes
Using a combinatorial approach to studying the hyperplane sections of Grassmannians, we give two new proofs of a result of Nogin concerning the higher weights of Grassmann codes. As a consequence, we obtain a bound on the number of higher dimensional subcodes of the Grassmann code having the minimum Hamming norm. We also discuss a generalization of Grassmann codes .
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We consider the question of determining the higher weights or the generalized Hamming weights of affine Grassmann codes and their duals. Several initial as well as terminal higher weights of affine Grassmann codes of an arbitrary level are determined explicitly. In the case of duals of these codes, we give a formula for many initial as well as terminal higher weights. As a special case, we obta...
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For integers m ≥ p ≥ 2, let GR = GR(m,m + p) ⊂ RP N be the Plücker embedding of the Grassmannian of m-subspaces in Rm+p . We consider a central projection of GR into a projective space RP mp of the same dimension as GR . Although GR may be non-orientable, the topological degree of this projection can be properly defined. Its values are unsigned integers. It turns out that when mp is even, the d...
متن کاملHigher weights of Grassmann codes in terms of properties of Schubert unions
We describe the higher weights of the Grassmann codes G(2, m) over finite fields Fq in terms of properties of Schubert unions, and in each case we determine the weight as the minimum of two explicit polynomial expressions in q.
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ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2009
ISSN: 1071-5797
DOI: 10.1016/j.ffa.2008.08.001