@article{Oztas2025, 
author = {Elif Segah Oztas and Amal S. Alali and Shakir Ali and Mohd Azeem and Muhammad S. M. Asri and Kok Bin Wong},
title = {On the construction of reversible DNA codes over        F                  4                  2          m                     via        T    n  -set codes},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {12},
pages = {29424-29453},
keywords = {reversible code, DNA code, reversible DNA code, Tn-set code, l-MDS code},
url = {https://www.sciopen.com/article/10.3934/math.20251292},
doi = {10.3934/math.20251292},
abstract = {The main objective of this paper is to introduce a new approach for constructing reversible and reversible DNA codes over the finite fields        F                  4                  2          m                    ,    m  ≥  1 from any given polynomials by utilizing        T    n  -set codes. Notably, these polynomials are not required to be self-reciprocal divisors of        x    n    −  1. In addition to this method, we provide some results that demonstrate how to generate reversible and reversible DNA codes from any    [  n  ,  k  ,  d  ]-cyclic codes over        F                  4                  2          m                     by applying        T    n  -set codes. Moreover, this approach allows us to determine a lower bound for the distance before completing the entire calculation process. We also construct a correspondence table between DNA sequences made up of    20-bases and all    256 elements of the linear code    ⟨      T          g        5    ∣      T          (              g                  ∗                            )                  ∘          4                      5    ⟩ over        F          16      , where    g  =      w          13        +  x  +      w    2        x    2    +      w    3        x    3   is a polynomial in    x over        F          16       and    (      g          ∗            )          ∘      4       represents the Hadamard        4          t      h      -power of the reciprocal polynomial        g          ∗       to demonstrate the fact that non-reversible codes may correspond to reversible DNA codes. Additionally, we provide a detailed table presenting some outcomes related to    l-MDS codes, self-orthogonal codes, and their associated parameters.}
}