Enumerative Encoding in the Grassmannian Space

Details Enumerative Encoding in the Grassmannian Space Enumerative Encoding in the Grassmannian Space

2009-03-09

arxiv.org/abs/0903.1556v1

Computer Science

Information Theory

2009 Informaton Theory Workshop, Taormina

Scientific paper

Codes in the Grassmannian space have found recently application in network coding. Representation of $k$-dimensional subspaces of $\F_q^n$ has generally an essential role in solving coding problems in the Grassmannian, and in particular in encoding subspaces of the Grassmannian. Different representations of subspaces in the Grassmannian are presented. We use two of these representations for enumerative encoding of the Grassmannian. One enumerative encoding is based on Ferrers diagrams representation of subspaces; and another is based on identifying vector and reduced row echelon form representation of subspaces. A third method which combine the previous two is more efficient than the other two enumerative encodings.

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