在 $$GR(2^{3},d)[X]/\langle X^{2},2X \rangle$$ 上的 DNA 编码

IF 0.6 4区工程技术 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Applicable Algebra in Engineering Communication and Computing Pub Date : 2024-07-13 DOI:10.1007/s00200-024-00667-1

C. Álvarez-García, C. A. Castillo-Guillén, Mohamed Badaoui

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引用次数: 0

摘要

本文的主要成果体现在两个方面。首先，确定了长度为 4 的有限局部环族，其最大理想的湮灭子长度为 2。第二，描述了这些环上的常环码、可逆码和 DNA 码的结构，码的长度与环的残差域的特征相对为素数。

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DNA codes over $$GR(2^{3},d)[X]/\langle X^{2},2X \rangle$$

The main results of this paper are in two directions. First, the family of finite local rings of length 4 whose annihilator of their maximal ideals have length 2 is determined. Second, the structure of constacyclic, reversible and DNA codes over those rings are described, the length of the code is relatively prime to the characteristic of the residue field of the ring.

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来源期刊

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

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.