Linear codes over Z4 + uZ4: MacWilliams identities, projections, and formally self-dual codes

Bahattin Yildiz, Suat Karadeniz

Research output: Contribution to journalArticlepeer-review

46 Scopus citations

Abstract

Linear codes are considered over the ring Z4+uZ4, a non-chain extension of Z4. Lee weights, Gray maps for these codes are defined and MacWilliams identities for the complete, symmetrized and Lee weight enumerators are proved. Two projections from Z4+uZ4 to the rings Z4 and F2+uF2 are considered and self-dual codes over Z4+uZ4 are studied in connection with these projections. A non-linear Gray map from Z4+uZ4 to (F2+uF2)2 is defined together with real and complex lattices associated to codes over Z4+uZ4. Finally three constructions are given for formally self-dual codes over Z4+u Z4 and their Z4-images together with some good examples of formally self-dual Z4-codes obtained through these constructions.

Original languageEnglish (US)
Pages (from-to)24-40
Number of pages17
JournalFinite Fields and Their Applications
Volume27
DOIs
StatePublished - May 2014
Externally publishedYes

Keywords

  • Codes over rings
  • Complete weight enumerator
  • Formally self-dual codes
  • Lifts
  • MacWilliams identities
  • Projections

ASJC Scopus subject areas

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

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