Open Access
3- https://doi.org/10.1007/s10623-022-01067-7
Reversible $$G^k$$-codes with applications to DNA codes
- Jun 24, 2022
- Designs, Codes and Cryptography
- Adrian Korban +2 more
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 \(G^k\)-codes of length kn, where \(k, n \in \mathbb {N},\) over the finite commutative Frobenius ring R. We employ our construction method to obtain many DNA codes over \(\mathbb {F}_4\) that satisfy the Hamming distance, the reverse, the 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 DNA codes of lengths 48, 56, 60, 64 and 72 for some fixed values of the Hamming distance d.
- # DNA Codes
- # Sizes Of Codes
- # Codes Of Lengths
- # Hamming Distance
- # Construction Method
- # Finite Commutative Ring
- # Values Of Distance
- # Commutative Ring
- # Matrix Construction Method
- # Frobenius Ring
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