Reversible and Reversible-Complement Double Cyclic Codes over F4+vF4 and its Application to DNA Codes
By: Divya Acharya, Prasanna Poojary, Vadiraja Bhatta G. R
In this article, we study the algebraic structure of double cyclic codes of length $(m, n)$ over $\mathbb{F}_4$ and we give a necessary and sufficient condition for a double cyclic code over $\mathbb{F}_4$ to be reversible. Also, we determine the algebraic structure of double cyclic codes of length $(m, n)$ over $\mathbb{F}_4+v\mathbb{F}_4$ with $v^2=v$, satisfying the reverse constraint and the reverse-complement constraint. Then we establish a one-to-one correspondence $ψ$ between the 16 DNA double pairs $S_{D_{16}} $ and the 16 elements of the finite ring $\mathbb{F}_4+v\mathbb{F}_4$. We also discuss the GC-content of DNA double cyclic codes.
Similar Papers
Construction of DNA codes using $θ$-skew cyclic codes over $\mathbb{F}_4 + v \mathbb{F}_4$
Information Theory
Makes DNA codes work better for computers.
On Algebraic Approaches for DNA Codes with Multiple Constraints
Information Theory
Stores more information in DNA.
$(Θ, Δ_Θ, \mathbf{a})$-cyclic codes over $\mathbb{F}_q^l$ and their applications in the construction of quantum codes
Information Theory
Creates better codes for computers and quantum computers.