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

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

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 Hammi...

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Hauptverfasser: Linial, Nati, Loyfer, Elyassaf
Format: Artikel
Sprache:eng
Schlagworte:
Computer Science - Information Theory
Mathematics - Information Theory
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Zusammenfassung: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.
DOI:10.48550/arxiv.2303.16619