Erzincan Üniversitesi Erzincan University Fen Bilimleri Enstitüsü Dergisi Journal of Science and Technology 2020, 13(3), 1383-1388 2020, 13(3), 1383-1388 ISSN: 1307-9085, e-ISSN: 2149-4584 Araştırma Makalesi DOI: 10.18185/erzifbed.635699 Research Article 1383 On the Reversibility Problem Yasemin ÇENGELLENMİŞ 1 , Abdullah DERTLİ 2* 1 Trakya University, Faculty of Sciences, Mathematics Department, Edirne, Turkey 2 Ondokuz Mayıs University, Faculty of Arts and Sciences, Mathematics Department, Samsun, Turkey Geliş / Received: 21/10/2019, Kabul / Accepted: 17/09/2020 Abstract By defining a non-trivial automorphism over 4 4 4 4 , R Z uZ vZ uvZ     where 2 2 , , u uv v uv vu    , and 4 {0,1, 2, 3} Z  , the skew cyclic codes over the finite ring R are introduced. By using the skew cyclic codes over R , it is solved the reversibility problem for DNA 4-bases. Thanks to this, the reversible DNA codes are obtained. Keywords: Skew cyclic codes, Reversibility problem. Ters Sıralama Problemi Hakkında Öz Bu çalışmada, 2 2 , , u uv v uv vu    ve 4 {0,1, 2, 3} Z  olmak üzere 4 4 4 4 R Z uZ vZ uvZ     sonlu halkası üzerinde aşikar olmayan bir otomorfizma tanımlanarak R halkası üzerinde çarpık devirli kodlar verilmiştir. R halkası üzerinde çarpık devirli kodlar kullanılarak DNA 4-bazlar için ters sıralama problemi çözülmüştür. Bu sayede ters sıralı DNA kodlar elde edilmiştir. Anahtar Kelimeler: Çarpık devirli kodlar, Ters sıralama problemi. 1. Introduction The transmission and storage of information take place in digital platform and the coding theory is necessary in order to correct and detect errors in the platform. There is another platform. In the platform, the correcting and detecting errors are necessary but it does not take place in digital. It is DNA. The idea of computing with DNA was given by T. Head (Head, 1987). L.Adleman performed the computation using DNA strands (Adleman, 1994). In fact, DNA sequence has four bases which are ( A ) Adenine, ( G ) Guanine, ( T ) Thymine and ( C ) Cytosine. DNA has also two strands. They are related by the Watson Crick Complement rule , , , c c c c A TT AC GG C     .