Linear programming bounds for codes via a covering argument

Michael Navon, Alex Samorodnitsky*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

Abstract

We recover the first linear programming bound of McEliece, Rodemich, Rumsey, and Welch for binary error-correcting codes and designs via a covering argument. It is possible to show, interpreting the following notions appropriately, that if a code has a large distance, then its dual has a small covering radius and, therefore, is large. This implies the original code to be small. We also point out that this bound is a natural isoperimetric constant of the Hamming cube, related to its Faber-Krahn minima. While our approach belongs to the general framework of Delsarte's linear programming method, its main technical ingredient is Fourier duality for the Hamming cube. In particular, we do not deal directly with Delsarte's linear program or orthogonal polynomial theory.

Original languageAmerican English
Pages (from-to)199-207
Number of pages9
JournalDiscrete and Computational Geometry
Volume41
Issue number2
DOIs
StatePublished - Mar 2009

Bibliographical note

Funding Information:
This research was partially supported by ISF grant 039-7682.

Keywords

  • Discrete Fourier transform
  • Linear programming bounds for codes

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