Coding Theory: On the VC-Dimension of Binary Error-Correcting Codes

שוהאנג הו (אונ' תל-אביב)
יום ראשון, 23.4.2017, 14:30
טאוב 601

We investigate the 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 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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