Coding Theory: On the VC-Dimension of Binary Error-Correcting Codes
- Sihuang Hu (Tel Aviv University)
- Sunday, 23.4.2017, 14:30
- Taub 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.