7 research outputs found
Skew cyclic codes over with derivation: structural properties and computational results
In this work, we study a class of skew cyclic codes over the ring
where with an automorphism
and a derivation namely codes as modules over a skew
polynomial ring whose multiplication is defined
using an automorphism and a derivation We
investigate the structures of a skew polynomial ring
We define -cyclic codes as a
generalization of the notion of cyclic codes. The properties of
-cyclic codes as well as dual -cyclic codes
are derived. As an application, some new linear codes over with
good parameters are obtained by Plotkin sum construction, also via a Gray map
as well as residue and torsion codes of these codes.Comment: 25 page
On DNA Codes Over the Non-Chain Ring with
In this paper, we present a novel design strategy of DNA codes with length
over the non-chain ring
with elements and , where denotes the length of a code over
. We first study and analyze a distance conserving map defined over the ring
into the length- DNA sequences. Then, we derive some conditions on the
generator matrix of a linear code over , which leads to a DNA code with
reversible, reversible-complement, homopolymer -run-length, and
-GC-content constraints for integer ().
Finally, we propose a new construction of DNA codes using Reed-Muller type
generator matrices. This allows us to obtain DNA codes with reversible,
reversible-complement, homopolymer -run-length, and -GC-content
constraints.Comment: This paper has been presented in IEEE Information Theory Workshop
(ITW) 2022, Mumbai, INDI
Reversible DNA codes from skew cyclic codes over a ring of order 256
We introduce skew cyclic codes over the finite ring , where and use them to construct reversible DNA codes. The 4-mers are matched with the elements of this ring. The reversibility problem for DNA 4-bases is solved and some examples are provided
Kernel Code for DNA Digital Data Storage
The biggest challenge when using DNA as a storage medium is maintaining its
stability. The relative occurrence of Guanine (G) and Cytosine (C) is essential
for the longevity of DNA. In addition to that, reverse complementary base pairs
should not be present in the code. These challenges are overcome by a proper
choice of group homomorphisms. Algorithms for storage and retrieval of
information in DNA stings are written by using kernel code. Complexities of
these algorithms are less compared to the existing algorithms. Construction
procedures followed in this paper are capable of constructing codes of required
sizes and Reverse complement distance.Comment: 12 pages, 1 figur