#16546: Enumeration of non-isomorphic scalar linear network codes over arbitrary
finite fields for multi-source multi-sink network coding (MSNC) problem.
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Reporter: Jayant | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.4
Component: matroid theory | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/Jayant/ticket/16546 | 6dd617ec010f39b2f55ceac55510f6d851b5d06d
Dependencies: | Stopgaps:
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Description changed by Jayant:
Old description:
> Given an instance of MSNC problem (a directed acyclic graph, a set of
> source nodes, a set of sink nodes, each source node having some source
> variables and each sink node wanting some source variables). Use single
> element extension of matroids to enumerate the codes with additional
> option to compute the rate region (set of all rate tuples) achievable
> over given finite field.
New description:
Given an instance of MSNC problem (a directed acyclic graph, a set of
source nodes, a set of sink nodes, each source node having some source
variables and each sink node wanting some source variables). Use single
element linear extensions of matroids to enumerate the codes satisfying
network constraints on the rank function with following additional
options:
1) Compute the rate region (set of all rate tuples) achievable over given
finite field via scalar linear codes
2) Construct scalar linear codes for achieving a given point in the rate
region (thereby determining scalar linear solvability of a network and the
property of being matroidal over a certain field)
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Ticket URL: <http://trac.sagemath.org/ticket/16546#comment:13>
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