Hamilton l-cycles in randomly perturbed hypergraphs

We prove that for integers 2 <= l < k and a small constant c, if a k-uniform hypergraph with linear minimum codegree is randomly 'perturbed' by changing non-edges to edges independently at random with probability p >= O(n(-(k-l)-c)) then with high probability the resulting k-uniform hypergraph contains a Hamilton l-cycle. This complements a recent analogous result for Hamilton 1-cycles due to Krivelevich, Kwan and Sudakov, and a comparable theorem in the graph case due to Bohman, Frieze and Martin.