The asymptotic rate vs. distance problem is a long-standing fundamental problem in coding theory. The best upper bound to date was given in 1977 and has received since then numerous proofs and interpretations. Here we provide a new, elementary proof of this bound based on counting walks in the Hamming cube.

翻译：码率与距离的渐近关系问题是编码理论中长期存在的根本性问题。目前最佳的上界于1977年提出，此后涌现出多种证明和解释方式。本文基于汉明立方体中的游走计数，给出了该上界的一个新的初等证明。