On reversible DNA codes over the ring $${\mathbb {Z}}_4[u,v]/\langle u^2-2,uv-2,v^2,2u,2v\rangle$$ based on the deletion distance

IF 0.6 4区 工程技术 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Hai Q. Dinh, Mohammad Ashraf, Washiqur Rehman, Ghulam Mohammad, Mohd Asim
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引用次数: 0

Abstract

Let \({\mathfrak {R}}= {\mathbb {Z}}_4[u,v]/\langle u^2-2,uv-2,v^2,2u,2v\rangle\) be a ring, where \({\mathbb {Z}}_{4}\) is a ring of integers modulo 4. This ring \({\mathfrak {R}}\) is a local non-chain ring of characteristic 4. The main objective of this article is to construct reversible cyclic codes of odd length n over the ring \({\mathfrak {R}}.\) Employing these reversible cyclic codes, we obtain reversible cyclic DNA codes of length n, based on the deletion distance over the ring \({\mathfrak {R}}.\) We also construct a bijection \(\Gamma\) between the elements of the ring \({\mathfrak {R}}\) and \(S_{D_{16}}.\) As an application of \(\Gamma ,\) the reversibility problem which occurs in DNA k-bases has been solved. Moreover, we introduce a Gray map \(\Psi _{\hom }:{\mathfrak {R}}^{n}\rightarrow {\mathbb {F}}_{2}^{8n}\) with respect to homogeneous weight \(w_{\hom }\) over the ring \({\mathfrak {R}}\). Further, we discuss the GC-content of DNA cyclic codes and their deletion distance. Moreover, we provide some examples of reversible DNA cyclic codes.

Abstract Image

基于删除距离的环 $${mathbb {Z}}_4[u,v]/angle u^2-2,uv-2,v^2,2u,2v\rangle$$ 上的可逆 DNA 编码
让({\mathfrak {R}}= {\mathbb {Z}}_4[u,v]/\langle u^2-2,uv-2,v^2,2u,2v\rangle\ )是一个环,其中({\mathbb {Z}}_{4}\ )是一个整数模为 4 的环。这个环 ({\mathfrak {R}}\ )是特性为 4 的局部非链环。本文的主要目的是在环({\mathfrak {R}}\)上构造奇数长度为 n 的可逆循环码。利用这些可逆循环码,我们得到了长度为 n 的可逆循环 DNA 码,其基础是环({\mathfrak {R}}\)上的删除距离。\我们还在环\({mathfrak {R}}\) 和 \(S_{D_{16}}.\)的元素之间构建了一个双投影\(\Gamma\) 作为\(\Gamma ,\)的应用,解决了DNA k碱基中出现的可逆性问题。此外,我们还在环({/mathfrak {R}}^{n}\rightarrow {\mathbb {F}}_{2}^{8n}/)上引入了关于同质权重\(w_{/hom }\) 的格雷映射(\Psi _{\hom }:{\mathfrak {R}}^{n}\rightarrow {\mathbb {F}}_{2}^{8n}\ )。此外,我们还讨论了 DNA 循环编码的 GC 含量及其删除距离。此外,我们还提供了一些可逆 DNA 循环码的例子。
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来源期刊
Applicable Algebra in Engineering Communication and Computing
Applicable Algebra in Engineering Communication and Computing 工程技术-计算机:跨学科应用
CiteScore
2.90
自引率
14.30%
发文量
48
审稿时长
>12 weeks
期刊介绍: Algebra is a common language for many scientific domains. In developing this language mathematicians prove theorems and design methods which demonstrate the applicability of algebra. Using this language scientists in many fields find algebra indispensable to create methods, techniques and tools to solve their specific problems. Applicable Algebra in Engineering, Communication and Computing will publish mathematically rigorous, original research papers reporting on algebraic methods and techniques relevant to all domains concerned with computers, intelligent systems and communications. Its scope includes, but is not limited to, vision, robotics, system design, fault tolerance and dependability of systems, VLSI technology, signal processing, signal theory, coding, error control techniques, cryptography, protocol specification, networks, software engineering, arithmetics, algorithms, complexity, computer algebra, programming languages, logic and functional programming, algebraic specification, term rewriting systems, theorem proving, graphics, modeling, knowledge engineering, expert systems, and artificial intelligence methodology. Purely theoretical papers will not primarily be sought, but papers dealing with problems in such domains as commutative or non-commutative algebra, group theory, field theory, or real algebraic geometry, which are of interest for applications in the above mentioned fields are relevant for this journal. On the practical side, technology and know-how transfer papers from engineering which either stimulate or illustrate research in applicable algebra are within the scope of the journal.
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