On The Vc-dimension Of Binary Codes
Hu Sihuang, Weinberger Nir, Shayevitz Ofer. SIAM J. Discrete Math. 2017
[Paper]
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.
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