Cyclic DNA codes over the ring   $\mathbb{Z}_4+u\mathbb{Z}_4+u^2\mathbb{Z}_4$

Karthick, G.; Gupta, Somi; Mohan, Cruz; Guenda, Kenza; Durairajan, C.

doi:10.13069/jacodesmath.1000959

Cited by 3 publications

(1 citation statement)

References 18 publications

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“…Rocha et al [32] analyzed the DNA sequence generated by linear codes over the ring Z 4 . Bennenni et al [33], Dinh et al [34], and Gowthaman et al [35] investigated DNA cyclic codes over rings.…”

Section: Error Correctionmentioning

confidence: 99%

An Analysis of Algebraic Codes over Lattice Valued Intuitionistic Fuzzy Type-3 $R$ -Submodules

Riaz

Kousar

Kausar

et al. 2022

Computational Intelligence and Neuroscience

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In the last few decades, the algebraic coding theory found widespread applications in various disciplines due to its rich fascinating mathematical structure. Linear codes, the basic codes in coding theory, are significant in data transmission. In this article, the authors’ aim is to enlighten the reader about the role of linear codes in a fuzzy environment. Thus, the reader will be aware of linear codes over lattice valued intuitionistic fuzzy type-3 (LIF-3) R-submodule and α -intuitionistic fuzzy ( α -IF) submodule. The proof that the level set of LIF-3 is contained in the level set of α -IF is given, and it is exclusively employed to define linear codes over α -IF submodule. Further, α -IF cyclic codes are presented along with their fundamental properties. Finally, an application based on genetic code is presented, and it is found that the technique of defining codes over α -IF submodule is entirely applicable in this scenario. More specifically, a mapping from the ℤ 64 module to a lattice L (comprising 64 codons) is considered, and α -IF codes are defined along with the respective degrees.

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Section: Error Correctionmentioning

confidence: 99%

An Analysis of Algebraic Codes over Lattice Valued Intuitionistic Fuzzy Type-3 $R$ -Submodules

Riaz

Kousar

Kausar

et al. 2022

Computational Intelligence and Neuroscience

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DNA codes over groups

Álvarez-García,

Castillo-Guillén,

Badaoui

et al. 2024

Des. Codes Cryptogr.

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Cyclic codes over non-chain ring $ \mathcal{R}(\alpha_1, \alpha_2, \ldots, \alpha_s) $ and their applications to quantum and DNA codes

Ali,

Alali,

Wong

et al. 2024

MATH

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<abstract><p>Let $ s \geq 1 $ be a fixed integer. In this paper, we focus on generating cyclic codes over the ring $ \mathcal{R}(\alpha_1, \alpha_2, \ldots, \alpha_s) $, where $ \alpha_i \in \mathbb{F}_q\backslash \{0\} $, $ 1 \leq i \leq s $, by using the Gray map that is defined by the idempotents. Moreover, we describe the process to generate an idempotent by using the formula (2.1). As applications, we obtain both optimal and new quantum codes. Additionally, we solve the DNA reversibility problem by introducing $ \mathbb{F}_q $ reversibility. The aim to introduce the $ \mathbb{F}_q $ reversibility is to describe IUPAC nucleotide codes, and consequently, 5 IUPAC DNA bases are considered instead of 4 DNA bases $ (A, \; T, \; G, \; C) $.</p></abstract>

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Cyclic DNA codes over the ring $\mathbb{Z}_4+u\mathbb{Z}_4+u^2\mathbb{Z}_4$

Cited by 3 publications

References 18 publications

An Analysis of Algebraic Codes over Lattice Valued Intuitionistic Fuzzy Type-3 $R$ -Submodules

An Analysis of Algebraic Codes over Lattice Valued Intuitionistic Fuzzy Type-3 $R$ -Submodules

DNA codes over groups

Cyclic codes over non-chain ring $ \mathcal{R}(\alpha_1, \alpha_2, \ldots, \alpha_s) $ and their applications to quantum and DNA codes

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Cyclic DNA codes over the ring $\mathbb{Z}_4+u\mathbb{Z}_4+u^2\mathbb{Z}_4$

Cited by 3 publications

References 18 publications

An Analysis of Algebraic Codes over Lattice Valued Intuitionistic Fuzzy Type-3 R -Submodules

An Analysis of Algebraic Codes over Lattice Valued Intuitionistic Fuzzy Type-3 R -Submodules

DNA codes over groups

Cyclic codes over non-chain ring $ \mathcal{R}(\alpha_1, \alpha_2, \ldots, \alpha_s) $ and their applications to quantum and DNA codes

Contact Info

Product

Resources

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An Analysis of Algebraic Codes over Lattice Valued Intuitionistic Fuzzy Type-3 $R$ -Submodules

An Analysis of Algebraic Codes over Lattice Valued Intuitionistic Fuzzy Type-3 $R$ -Submodules