we want to use some of this properties to explain the existence ways for Decomposition of binary codes..
Please define what you mean by "matroidal network". Do you wish to attach a graph to a matroid?
geometrically, A graphical representation of matroid has some properties of network. The existence of corresponding vector linear index codes linked to the matroid multilinear representations.in fact Matroidal Networks Associated with
Representable Matroids.
i want to find a new method on decomposition of binary codes via geometrically properties of network that is related to matroid.
A graph is defined by a vertex set and an adjacency relation. Please define both in this case of "matroidal network".
This is a good question.
Pursuing further what @Patrick Solé has observed, consider
A.E. Kim, On Network Coding Capacity--Matroidal Networks and Network Capacity Regions, M.Sc. thesis, MIT, 2010:
http://web.stanford.edu/~tonyekim/Thesis_NetworkCoding.pdf
See Def. 37 (Polytope reconstruction problem), where the computation of network routing capacity region is recast as the polytope reconstruction problem with a ray oracle (p. 38).
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