Estimates of the distance distribution of codes and designs

A. Ashikhmin*, A. Barg, S. Litsyn

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the problem of bounding the distance distribution for unrestricted block codes with known distance and/or dual distance. Applying the polynomial method, we provide a general framework for previously known results. We derive several upper and lower bounds both for finite length and for sequences of codes of growing length. Asymptotic results in the paper improve previously known estimates. In particular, we prove the best known bounds on the binomiality range of the distance spectrum of codes with a known dual distance.

Original languageEnglish
Pages (from-to)1050-1061
Number of pages12
JournalIEEE Transactions on Information Theory
Volume47
Issue number3
DOIs
StatePublished - Mar 2001
Externally publishedYes

Keywords

  • Binomial spectrum
  • Constant weight codes
  • Distance distribution
  • Krawtchouk polynomials
  • Polynomial method

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