Reversible cyclic codes over some finite rings and their application to DNA codes

2021 ◽  
Vol 40 (7) ◽  
Author(s):  
Om Prakash ◽  
Shikha Patel ◽  
Shikha Yadav
Keyword(s):  
Cyclic Codes ◽  
Finite Rings ◽  
Dna Codes ◽  
Reversible Cyclic Codes

DNA computing over the ring ℤ4[v]/〈v2 − v〉

2018 ◽  
Vol 11 (07) ◽  
pp. 1850090
Author(s):  
Narendra Kumar ◽  
Abhay Kumar Singh
Keyword(s):  
Significant Role ◽  
Dna Computing ◽  
Linear Codes ◽  
Cyclic Codes ◽  
Finite Ring ◽  
Dna Codes ◽  
Reversible Cyclic Codes ◽  
Text Images

In this paper, we discuss the DNA construction of general length over the finite ring [Formula: see text], with [Formula: see text], which plays a very significant role in DNA computing. We discuss the GC weight of DNA codes over [Formula: see text]. Several examples of reversible cyclic codes over [Formula: see text] are provided, whose [Formula: see text]-images are [Formula: see text]-linear codes with good parameters.

scholarly journals On cyclic DNA codes over the rings Z4 + wZ4 and Z4 + wZ4 + vZ4 + wvZ4

BIOMATH ◽  
2017 ◽  
Vol 6 (2) ◽  
pp. 1712167 ◽  
Author(s):  
Abdullah Dertli ◽  
Yasemin Cengellenmis
Keyword(s):  
Cyclic Codes ◽  
Finite Ring ◽  
Finite Rings ◽  
Binary Images ◽  
Dna Codes ◽  
Reverse Complement ◽  
Skew Cyclic Codes ◽  
Cyclic Dna Codes

The structures of cyclic DNA codes of odd length over the finite rings R = Z4 + wZ4, w^2 = 2 and S = Z4 + wZ4 + vZ4 + wvZ4; w^2 = 2; v^2 =v; wv = vw are studied. The links between the elements of the rings R, S and 16 and 256 codons are established, respectively. The cyclic codes of odd length over the finite ring R satisfy reverse complement constraint and the cyclic codes of odd length over the finite ring S satisfy reverse constraint and reverse complement constraint are studied. The binary images of the cyclic DNA codes over the finite rings R and S are determined. Moreover, a family of DNA skew cyclic codes over R is constructed, its property of being reverse complement is studied.

scholarly journals New quantum codes from dual-containing cyclic codes over finite rings

2016 ◽  
Vol 15 (11) ◽  
pp. 4489-4500 ◽  
Author(s):  
Yongsheng Tang ◽  
Shixin Zhu ◽  
Xiaoshan Kai ◽  
Jian Ding
Keyword(s):  
Cyclic Codes ◽  
Quantum Codes ◽  
Finite Rings

scholarly journals Constacyclic and Linear Complementary Dual Codes Over Fq + uFq

2020 ◽  
Vol 70 (6) ◽  
pp. 626-632
Author(s):  
Om Prakash ◽  
Shikha Yadav ◽  
Ram Krishna Verma
Keyword(s):  
Cyclic Codes ◽  
Gray Map ◽  
Constacyclic Codes ◽  
Dual Codes ◽  
Gray Image ◽  
New Class ◽  
Sharing Scheme ◽  
Lcd Codes ◽  
Reversible Cyclic Codes

This article discusses linear complementary dual (LCD) codes over ℜ = Fq+uFq(u2=1) where q is a power of an odd prime p. Authors come up with a new Gray map from ℜn to F2nq and define a new class of codes obtained as the gray image of constacyclic codes over .ℜ Further, we extend the study over Euclidean and Hermitian LCD codes and establish a relation between reversible cyclic codes and Euclidean LCD cyclic codes over ℜ. Finally, an application of LCD codes in multisecret sharing scheme is given.

scholarly journals Skew cyclic codes over 𝔽4R

2020 ◽  
pp. 2250065
Author(s):  
Nasreddine Benbelkacem ◽  
Martianus Frederic Ezerman ◽  
Taher Abualrub ◽  
Nuh Aydin ◽  
Aicha Batoul
Keyword(s):  
Error Control ◽  
Cyclic Codes ◽  
Gray Map ◽  
Inner Product ◽  
Algebraic Structures ◽  
Error Control Codes ◽  
Dna Codes ◽  
Natural Connection ◽  
Skew Cyclic Codes

This paper considers a new alphabet set, which is a ring that we call [Formula: see text], to construct linear error-control codes. Skew cyclic codes over this ring are then investigated in details. We define a nondegenerate inner product and provide a criteria to test for self-orthogonality. Results on the algebraic structures lead us to characterize [Formula: see text]-skew cyclic codes. Interesting connections between the image of such codes under the Gray map to linear cyclic and skew-cyclic codes over [Formula: see text] are shown. These allow us to learn about the relative dimension and distance profile of the resulting codes. Our setup provides a natural connection to DNA codes where additional biomolecular constraints must be incorporated into the design. We present a characterization of [Formula: see text]-skew cyclic codes which are reversible complement.

scholarly journals New DNA Codes from Cyclic Codes over Mixed Alphabets

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1977
Author(s):  
Hai Q. Dinh ◽  
Sachin Pathak ◽  
Ashish Kumar Upadhyay ◽  
Woraphon Yamaka
Keyword(s):  
Cyclic Codes ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Block Length ◽  
Dna Codes ◽  
Reverse Complement ◽  
Gray Maps ◽  
Cyclic Dna Codes ◽  
One To One ◽  
Necessary And Sufficient

Let R=F4+uF4,withu2=u and S=F4+uF4+vF4,withu2=u,v2=v,uv=vu=0. In this paper, we study F4RS-cyclic codes of block length (α,β,γ) and construct cyclic DNA codes from them. F4RS-cyclic codes can be viewed as S[x]-submodules of Fq[x]⟨xα−1⟩×R[x]⟨xβ−1⟩×S[x]⟨xγ−1⟩. We discuss their generator polynomials as well as the structure of separable codes. Using the structure of separable codes, we study cyclic DNA codes. By using Gray maps ψ1 from R to F42 and ψ2 from S to F43, we give a one-to-one correspondence between DNA codons of the alphabets {A,T,G,C}2,{A,T,G,C}3 and the elements of R,S, respectively. Then we discuss necessary and sufficient conditions of cyclic codes over F4, R, S and F4RS to be reversible and reverse-complement. As applications, we provide examples of new cyclic DNA codes constructed by our results.

Sign in / Sign up

Export Citation Format

Share Document