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arXiv · 1703.01586

On the VC-Dimension of Binary Codes

Sihuang Hu·Nir Weinberger·Ofer Shayevitz
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Abstract

We investigate the asymptotic rates of length-$n$ binary codes with VC-dimension at most $dn$ and minimum distance at least $δn$. 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.

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Sihuang Hu, Nir Weinberger, Ofer Shayevitz. 2018-06-27. On the VC-Dimension of Binary Codes. https://doi.org/10.1137/18m116486x

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