Bounds for binary multiple covering codes

Heikki O. Hämäläinen, Iiro S. Honkala, Markku K. Kaikkonen, Simon N. Litsyn

Research output: Contribution to journalArticlepeer-review

Abstract

We study codes that are multiple coverings of the Hamming space {Mathematical expression} and discuss lower and upper bounds on K(n, r, μ), the minimum cardinality of a binary code of length n such that the Hamming spheres of radius r centered at the codewords cover {Mathematical expression} at least μ times. We also study the similar problem of multiple coverings containing repeated words. A table of bounds for n≤16, r≤4, μ≤4 is given.

Original languageEnglish
Pages (from-to)251-275
Number of pages25
JournalDesigns, Codes, and Cryptography
Volume3
Issue number3
DOIs
StatePublished - Jul 1993

Keywords

  • binary codes
  • multiple coverings

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