Reduction status of Cheung’s new constant-cost problem

Ascertain whether the constant-cost communication problem constructed by Tsun‑Ming Cheung (2024), which generalizes k‑Hamming Distance, reduces to a distance‑r composition of k‑Hamming Distance problems, or prove that it lies outside that framework.

Background

After the manuscript’s preparation, a new constant‑cost problem generalizing k‑Hamming Distance was introduced by Cheung. Its relationship to the distance‑r composition framework is unclear; establishing whether it reduces to this framework would clarify the boundary of known techniques and potentially provide a new paradigm for randomness usage in constant‑cost protocols.