On the Distance Distributions of BCH Codes and Their Duals

Ilia Krasikov, Simon Litsyn

Research output: Contribution to journalArticlepeer-review

Abstract

Based on new bounds on the values of Krawtchouk polynomials, we improve earlier known estimates for components of the distance distributions of BCH codes and their duals. Moreover, we show that if one uses estimates on Krawtchouk polynomials for bounding the error term in the binomial approximation to the distance distribution of BCH codes, the given results are actually the best possible. One of the advantages of the proposed approach is that it provides estimates with no restrictions on the minimum distance of the code.

Original languageEnglish
Pages (from-to)223-232
Number of pages10
JournalDesigns, Codes, and Cryptography
Volume23
Issue number2
DOIs
StatePublished - Jul 2001

Keywords

  • Bch codes
  • Distance distribution
  • Duals of bch codes
  • Krawtchouk polynomials

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