• Corpus ID: 235658079

The topology of projective codes and the distribution of zeros of odd maps

@inproceedings{Adams2021TheTO,
  title={The topology of projective codes and the distribution of zeros of odd maps},
  author={Henry Adams and Johnathan Bush and Florian Frick},
  year={2021}
}
. We show that the size of codes in projective space controls structural results for zeros of odd maps from spheres to Euclidean space. In fact, this relation is given through the topology of the space of probability measures on the sphere whose supports have diameter bounded by some specific parameter. Our main result is a generalization of the Borsuk–Ulam theorem, and we derive four consequences of it: (i) We give a new proof of a result of Simonyi and Tardos on topological lower bounds for… 

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