Leírás
Véges Geometria szeminárium
Abstract:
Mixed Hamming packings are considered: the maximal cardinality given a
minimum codeword Hamming distance of mixed codes is addressed via mixed
integer programming models. Adopting the concept of contact graph from
classical continuous sphere packing problems, a reduction technique for
the models is introduced, which enables their efficient solution. Some
of the improved dual bounds proved that already known packing
constructions for some mixed binary-ternary codes are optimal, like:
$N_{2,3}(4,3;d=3)=26$ and $N_{2,3}(7,1;d=3)=28$; both former upper
bounds were $30$. The corresponding QUBO models are likely to be the
smallest hard benchmark instances for Ising spin glass based quantum
computers in the near future.
Joint work with Mátyás Koniorczyk, an arXiv preprint is available at
https://arxiv.org/abs/2310.01883