In linearnetworkcoding the information is encoded in terms of a basis of a vector space and it is received as a basis of a possible altered vector space. In the constantdimension case Koetter and Kschischang introd...
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In linearnetworkcoding the information is encoded in terms of a basis of a vector space and it is received as a basis of a possible altered vector space. In the constantdimension case Koetter and Kschischang introduced a metric on the Grassmannian and proved efficient and correct decoding in terms of this metric. Here we introduce a second order invariant of the code: the minimum dimension of the linear span of 3 different linear subspaces belonging to the code. This is the case s = 3 of a family d(s) and d(s)', s >= 3, of invariants of network codes. We study these invariants in a case recently proposed by Hansen (the set of all osculating spaces of a Veronese embedding of a finite projective space) and for a related case (the set of osculating spaces to curves of positive genus) with a complete description of the case of elliptic curves and the ones related to the Hermitian curve.
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