On the VC-Dimension of Binary Codes
Information Theory
2018-08-31 v2 math.IT
Abstract
We investigate the asymptotic rates of length- binary codes with VC-dimension at most and minimum distance at least . Two upper bounds are obtained, one as a simple corollary of a result by Haussler and the other via a shortening approach combining Sauer-Shelah lemma and the linear programming bound. Two lower bounds are given using Gilbert-Varshamov type arguments over constant-weight and Markov-type sets.
Cite
@article{arxiv.1703.01586,
title = {On the VC-Dimension of Binary Codes},
author = {Sihuang Hu and Nir Weinberger and Ofer Shayevitz},
journal= {arXiv preprint arXiv:1703.01586},
year = {2018}
}