Reversible $$G^k$$-codes with applications to DNA codes

Korban, Adrian; Şahinkaya, Serap; Üstün, Deniz

doi:10.1007/s10623-022-01067-7

Cited by 3 publications

(2 citation statements)

References 17 publications

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“…Similarly, composition of DNA codes are studied over the rings F 2 + uF 2 in [13,14], F 2 + uF 2 + vF 2 + uvF 2 in [15], F 2 [u]/(u 2k − 1) in [16], Z 4 [v]/(v 2 − v) in [17], Z 4 [u]/< u 2 − 1 > in [18], Z 4 + vZ 4 in [19], F 2 [u]/(u 4 − 1) in [20] and F 4 [u]/< u 3 > in [21,22]. Further, DNA codes are studied over group matrix rings in [23] and Galois rings in [24].…”

Section: Introductionmentioning

confidence: 99%

DNA Images of Codes Over F4t [u]/<uk>

Sezer,

Yaraneri

2023

Preprint

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The aim of this paper is to study DNA codes using some Gray images of codes over the chain rings S = F4t [u]<uk > and R = F4[v]⁄<vtk>. The special cases t=1 and k=2,3 were studied before. We construct some nice Gray maps from R, S to DNA codewords, whose images satisfy complement and reversibility properties. Studying the general case allows us to construct codes with better parameters. Subsequently, we concentrate on codes over arbitrary commutative rings and cyclic codes over R and obtain some necessary and sufficient conditions equal to the common constraints on DNA codes, like reversibility. Moreover, a variety of sample codes over multiple rings are presented. MSC Classification: 11T71 , 94B05 , 94B15

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Section: Introductionmentioning

confidence: 99%

DNA Images of Codes Over F4t [u]/<uk>

Sezer,

Yaraneri

2023

Preprint

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“…Some known methods for designing good DNA codes include the study of reversible self-dual codes over GF (4) [21], the study of cyclic and extended cyclic constructions [1,2], the study of linear constructions [17], and the study of skew polynomial rings [18]. Recently in [11,15,23,25,24], linear codes derived from group ring elements were considered to construct reversible DNA codes that satisfy some constraints, and many new lower bounds of DNA codes of various lengths are found. This suggests that the study of group rings is an interesting research direction that may have some useful applications to DNA coding.…”

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confidence: 99%

DNA codes from skew dihedral group ring

Dougherty

Korban

Şahinkaya

et al. 2024

AMC

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<p style='text-indent:20px;'>In this work, we present a matrix construction for reversible codes derived from skew dihedral group rings. By employing this matrix construction, the ring <inline-formula><tex-math id="M1">\begin{document}$ \mathcal{F}_{j, k} $\end{document}</tex-math></inline-formula> and its associated Gray maps, we show how one can construct reversible codes of length <inline-formula><tex-math id="M2">\begin{document}$ n2^{j+k} $\end{document}</tex-math></inline-formula> over the finite field <inline-formula><tex-math id="M3">\begin{document}$ \mathbb{F}_4. $\end{document}</tex-math></inline-formula> As an application, we construct a number of DNA codes that satisfy the Hamming distance, the reverse, the reverse-complement, and the GC-content constraints with better parameters than some good DNA codes in the literature.</p>

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