Sharp bounds on $k$-wise generalizations of oddtowns and eventowns

Zichao Dong, Minghui Ouyang, Lan Wei

For $\hat{\mathbf{I}}\pm =(\hat{I}{\pm }_1,\dots ,\hat{I}{\pm }_k)\in {\mathbb{F}}_2^k$, an $\hat{\mathbf{I}}\pm$-town is a set family in which every $i$-wise intersection has parity $\hat{I}{\pm }_i$. Denote by $f_{\boldsym…