Codes over Rk, Gray maps and their binary images

Steven T. Dougherty, Bahattin Yildiz, Suat Karadeniz

Research output: Contribution to journalArticlepeer-review

55 Scopus citations

Abstract

We introduce codes over an infinite family of rings and describe two Gray maps to binary codes which are shown to be equivalent. The Lee weights for the elements of these rings are described and related to the Hamming weights of their binary image. We describe automorphisms in the binary image corresponding to multiplication by units in the ring and describe the ideals in the ring, using them to define a type for linear codes. Finally, Reed Muller codes are shown as the image of linear codes over these rings.

Original languageEnglish (US)
Pages (from-to)205-219
Number of pages15
JournalFinite Fields and Their Applications
Volume17
Issue number3
DOIs
StatePublished - May 2011
Externally publishedYes

Keywords

  • Automorphisms
  • Binary image
  • Codes over rings
  • Gray map
  • Optimal codes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Algebra and Number Theory
  • Engineering(all)
  • Applied Mathematics

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