On Hamilton cycle decompositions of r-uniform r-partite hypergraphs

The definition of edge-adjacency can be generalized in multiple ways to hypergraphs, and extended from that, cycles and Hamilton cycles. One such generalization of a Hamilton cycle is attributed to Kierstead and Katona. In a recent paper by Kuhl and Schroeder, Hamilton cycle decompositions of complete r-partite r-uniform hypergraphs are discussed, a conjecture was made that the necessary numerical conditions are sufficient, and was shown true for some cases. In this paper, the conjecture is proved using constructions involving Hamming codes, comparisons between the two constructions are made, and a classification of when they are equivalent is shown.