CORDIS Project
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This project explores dense packing problems in discrete mathematics, focusing on sphere packing in various dimensions. It aims to improve understanding of linear codes and their applications in error correction, while also investigating periodic sphere packings in metric spaces.
The packing problem associated with a family of sets F seeks a large subfamily of pairwise disjoint members of F.
When F comprises the unit balls in d-space, this is the sphere packing problem, which for d = 3 was solved by Hales-Ferguson (Keplers conjecture).
The cases d = 8, 24 have won Viazovska her Fields Medal.
Much of discrete mathematics deals with dense packing problems.
The asymptotic rate vs. distance problem, may be the most fundamental open problem about error correcting codes.
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