Reversible G-codes over the ring Fj,k with applications to DNA codes
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Tarih
2023
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
American Institute of Mathematical Sciences (AIMS)
Erişim Hakkı
info:eu-repo/semantics/restrictedAccess
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.
Açıklama
Anahtar Kelimeler
Group Codes, Linear Codes, Codes over Rings, Gray Maps, DNA Codes
Kaynak
Advances in Mathematics of Communications
WoS Q Değeri
Scopus Q Değeri
Cilt
17
Sayı
6
Künye
Cengellenmis, Y., Dertli, A., Dougherty, S.T., Korban, A., Şahinkaya, S. ve Ustun, D. (2023). Reversible G-codes over the ring with applications to DNA codes. Advances in Mathematics of Communications, 17(6): 1406-1421. doi: 10.3934/amc.2021056
