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

Nesibe Tufekci, Bahattin Yildiz

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

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
Volume66
Issue number6
DOIs
StatePublished - Dec 1 2016
Externally publishedYes

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

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