Fri, November 15, 2019
Public Access Category: All |
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- Time:
- 4:30pm-5:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- CACAAG seminar.
Speaker: Trygve Johnsen.
Affiliation: The Artic University of Norway.
Date and time: Friday 15 November, 4:30 pm - 5:30 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Greedy weights for codes and matroids.
Abstract: Greedy weights of linear codes measure the minimal support
cardinality
of chains of subcodes for a certain lexicographic order. We show how the
problem
of finding such weights can be studied by inspecting the poset of flats of
the generator matroid, or better: the (dual) poset of cycles for the
parity check matroid. The terms of a minimal resolution of the
Stanley-Reisner ring of the independence complex of the parity check
corresponds to the points of the poset. Optimal paths in the poset
diagram, and optimal chains of non-zero component maps in a minimal
resolution of the Stanley-Reisner ring. correspond to greedy weights Such
maps can be constructed using poset homology, or studied indirectly,
through the Taylor complex, which also provides a resolution, although
not minimal.