On the VC-dimension of binary codes

Sihuang Hu; Nir Weinberger; Ofer Shayevitz

doi:10.1137/18M116486X

On the VC-dimension of binary codes

Sihuang Hu, Nir Weinberger, Ofer Shayevitz

School of Electrical Engineering

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

We investigate the maximal asymptotic rates of length-n binary codes with VC-dimension at most dn and minimum distance at least \delta n. Two upper bounds are obtained, one as a simple corollary of a result by Haussler and the other via a shortening approach combining the 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.

Original language	English
Pages (from-to)	2161-2171
Number of pages	11
Journal	SIAM Journal on Discrete Mathematics
Volume	32
Issue number	3
DOIs	https://doi.org/10.1137/18M116486X
State	Published - 2018

Keywords

Gilbert-Varshamov bound
Sauer-Shelah lemma
Vapnik-Chervonenkis dimension

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1137/18M116486X

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title = "On the VC-dimension of binary codes",

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KW - Gilbert-Varshamov bound

KW - Sauer-Shelah lemma

KW - Vapnik-Chervonenkis dimension

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JO - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

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ER -

On the VC-dimension of binary codes

Abstract

Keywords

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