On codes over Rk,m and constructions for new binary self-dual codes

Nesibe Tufekci, Bahattin Yildiz

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


In this work, we study codes over the ring Rk,m = F2[u, v]/ uk, vm, uv - vu, which is a family of Frobenius, characteristic 2 extensions of the binary field. We introduce a distance and duality preserving Gray map from Rk, m to F2km together with a Lee weight. After proving the MacWilliams identities for codes over Rk,m for all the relevant weight enumerators, we construct many binary self-dual codes as the Gray images of self-dual codes over Rk,m. In addition to many extremal binary self-dual codes obtained in this way, including a new construction for the extended binary Golay code, we find 175 new Type I binary self-dual codes of parameters [72, 36, 12] and 105 new Type II binary self-dual codes of parameter [72, 36, 12].

Original languageEnglish (US)
Pages (from-to)1511-1526
Number of pages16
JournalMathematica Slovaca
Issue number6
StatePublished - Dec 1 2016
Externally publishedYes


  • Gray maps
  • MacWilliams identities
  • codes over rings
  • extremal self-dual codes

ASJC Scopus subject areas

  • General Mathematics


Dive into the research topics of 'On codes over Rk,m and constructions for new binary self-dual codes'. Together they form a unique fingerprint.

Cite this