Estimates of the distance distribution of codes and designs

A. Ashikhmin, A. Barg, S. Litsyn

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)1-11
Number of pages11
JournalElectronic Notes in Discrete Mathematics
Volume6
StatePublished - 2000

Keywords

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

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