2 research outputs found
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
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