@article{Alsuraiheed2023, 
author = {Turki Alsuraiheed and Elif Segah Oztas and Shakir Ali and Merve Bulut Yilgor},
title = {Reversible codes and applications to DNA codes over        F                  4                  2          t                      [  u  ]      /    (      u    2    −  1  )},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {11},
pages = {27762-27774},
keywords = {reversible code, DNA code, r-glifted polynomial},
url = {https://www.sciopen.com/article/10.3934/math.20231421},
doi = {10.3934/math.20231421},
abstract = {Let    n  ≥  1 be a fixed integer. Within this study, we present a novel approach for discovering reversible codes over rings, leveraging the concept of    r-glifted polynomials. This technique allows us to achieve optimal reversible codes. As we extend our methodology to the domain of DNA codes, we establish a correspondence between    4  t-bases of DNA and elements within the ring        R          2      t        =      F                  4                  2          t                      [  u  ]      /    (      u          2        −  1  ). By employing a variant of    r-glifted polynomials, we successfully address the challenges of reversibility and complementarity in DNA codes over this specific ring. Moreover, we are able to generate reversible and reversible-complement DNA codes that transcend the limitations of being linear cyclic codes generated by a factor of        x    n    −  1.}
}