REVERSIBLE <i>G</i>-CODES OVER THE RING <i>F<sub>j,k</sub></i> WITH APPLICATIONS TO DNA CODES

ÇENGELLENMİŞ Y., Dertli A., Dougherty S. T., Korban A., Sahinkaya S., Ustun D.

ADVANCES IN MATHEMATICS OF COMMUNICATIONS, cilt.17, sa.6, ss.1406-1421, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 17 Sayı: 6
  • Basım Tarihi: 2023
  • Doi Numarası: 10.3934/amc.2021056
  • Dergi Adı: ADVANCES IN MATHEMATICS OF COMMUNICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Applied Science & Technology Source, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.1406-1421
  • Ondokuz Mayıs Üniversitesi Adresli: Evet

Özet

In this paper, we show that one can construct a G-code from group rings that is reversible. Specifically, we show that given a group with a subgroup of order half the order of the ambient group with an element that is its own inverse outside the subgroup, we can give an ordering of the group elements for which G-codes are reversible of index alpha. Additionally, we introduce a new family of rings, F-j,F-k, whose base is the finite field of order 4 and study reversible G-codes over this family of rings. Moreover, we present some possible applications of reversible G-codes over F-j,F-k to reversible DNA codes. We construct many reversible G-codes over F-4 of which some are optimal. These codes can be used to obtain reversible DNA codes.