An Elementary Proof of the First LP Bound on the Rate of Binary Codes

03/29/2023

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by   Nati Linial, et al.

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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.