scholarly journals Reversible DNA codes from skew cyclic codes over a ring of order 256

2021 ◽  
pp. 1-8
Author(s):  
Nuh AYDİN ◽  
Yasemin CENGELLENMİS ◽  
Abdullah DERTLİ
Keyword(s):  
Cyclic Codes ◽  
Dna Codes ◽  
Skew Cyclic Codes

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 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.

On skew cyclic codes over a mixed alphabet and their applications to DNA codes

2021 ◽  
pp. 2150143
Author(s):  
Abdullah Dertli ◽  
Yasemin Cengellenmis ◽  
Nuh Aydin
Keyword(s):  
Finite Field ◽  
Cyclic Code ◽  
Cyclic Codes ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Dna Codes ◽  
Skew Cyclic Codes ◽  
Necessary And Sufficient

In this paper, we introduce skew cyclic codes over the mixed alphabet [Formula: see text], where [Formula: see text] is the finite field with 4 elements and [Formula: see text]. Our results include a description of the generator polynomials of such codes and a necessary and sufficient condition for an [Formula: see text]-skew cyclic code to be reversible complement.

scholarly journals Hartmann–Tzeng bound and skew cyclic codes of designed Hamming distance

2018 ◽  
Vol 50 ◽  
pp. 84-112 ◽  
Author(s):  
José Gómez-Torrecillas ◽  
F.J. Lobillo ◽  
Gabriel Navarro ◽  
Alessando Neri
Keyword(s):  
Hamming Distance ◽  
Cyclic Codes ◽  
Skew 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.

A Note on Skew Cyclic Codes over a Class of Rings

2020 ◽  
Vol 27 (04) ◽  
pp. 703-712
Author(s):  
Hai Q. Dinh ◽  
Bac T. Nguyen ◽  
Songsak Sriboonchitta
Keyword(s):  
Finite Field ◽  
Cyclic Code ◽  
Cyclic Codes ◽  
General Setting ◽  
Constacyclic Codes ◽  
Arbitrary Length ◽  
Skew Cyclic Codes

We study skew cyclic codes over a class of rings [Formula: see text], where each [Formula: see text] [Formula: see text] is a finite field. We prove that a skew cyclic code of arbitrary length over R is equivalent to either a usual cyclic code or a quasi-cyclic code over R. Moreover, we discuss possible extension of our results in the more general setting of [Formula: see text]-dual skew constacyclic codes over R, where δR is an automorphism of R.

Skew Cyclic Codes over a Non-chain Ring

2017 ◽  
Vol 26 (3) ◽  
pp. 544-547 ◽  
Author(s):  
Minjia Shi ◽  
Ting Yao ◽  
Patrick Solé
Keyword(s):  
Cyclic Codes ◽  
Chain Ring ◽  
Skew Cyclic Codes

Skew cyclic codes over 𝔽p + u𝔽p

2018 ◽  
Vol 5 (1) ◽  
pp. 81
Author(s):  
R. Dastbasteh ◽  
H. Mousavi ◽  
T. Abualrub ◽  
N. Aydin ◽  
J. Haghighat
Keyword(s):  
Cyclic Codes ◽  
Skew Cyclic Codes
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