#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 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)
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 a source
message and each sink node wanting a subset of source messages). 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:14>
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