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The maximum size of an $r$-uniform hypergraph without a Berge cycle of lengthat least $k$ has been determined for all $k \ge r+3$ by F\"uredi, Kostochka andLuo and for $k<r$ (and $k=r$, asymptotically) by Kostochka and Luo. In thispaper, we settle the remaining cases: $k=r+1$ and $k=r+2$, proving a conjectureof F\"uredi, Kostochka and Luo.

Avoiding long Berge cycles, the missing cases $k=r+1$ and $k = r+2$