ZixiangXu

In 1966, Kleitman established that if $|A\mathrm{△}B|\le d$ for any $A,B\in \mathcal{F}$, then $|\mathcal{F}|\le \sum _{i=0}^k(\genfrac{}{}{0ex}{}{n}{i})$ for $d=2k$, and $|\mathcal{F}|\le 2\sum _{i=0}^k(\genfrac{}{}{0ex}{}{n-1}{i})$ for $d=2k+1$. These upper bounds are attained by the …