English

Reversible $G^k$-Codes with Applications to DNA Codes

Information Theory 2021-08-05 v1 math.IT

Abstract

In this paper, we give a matrix construction method for designing DNA codes that come from group matrix rings. We show that with our construction one can obtain reversible GkG^k-codes of length kn,kn, where k,nN,k, n \in \mathbb{N}, over the finite commutative Frobenius ring R.R. We employ our construction method to obtain many DNA codes over F4\mathbb{F}_4 that satisfy the Hamming distance, reverse, reverse-complement and the fixed GC-content constraints. Moreover, we improve many lower bounds on the sizes of some known DNA codes and we also give new lower bounds on the sizes of some DNA codes of lengths 48,56,60,6448, 56, 60, 64 and 7272 for some fixed values of the Hamming distance d.d.

Keywords

Cite

@article{arxiv.2108.02033,
  title  = {Reversible $G^k$-Codes with Applications to DNA Codes},
  author = {Adrian Korban and Serap Sahinkaya and Deniz Ustun},
  journal= {arXiv preprint arXiv:2108.02033},
  year   = {2021}
}
R2 v1 2026-06-24T04:49:27.936Z