#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 | b86855edae1d6bde8e2dc1a03d274737cc24c0ec
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 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)
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 non-
isomorphic 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:16>
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