ALICE physics projections for a short oxygen-beam run at the LHC

This document collects performance projections for a selection of measurements that can be carried out with a short O$-$O run during the LHC Run 3. The baseline centre-of-mass energy per nucleon$-$nucleon collision is $\sqrt{s_{\rm NN}}=6.37$ TeV and measurement uncertainties are given for the integrated luminosity $L_{\rm int}= 1$ nb$^{-1}$. Some projections for p$-$O collisions are also included. These studies were presented at the CERN workshop on Opportunities of O$-$O and p$-$O collisions at the LHC.