Designing DNA codes from reversible self-dual codes over <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e711" altimg="si5.svg"><mml:mrow><mml:mi>G</mml:mi><mml:mi>F</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mn>4</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>

Kim, Hyun Jin; Choi, Whan-Hyuk; Lee, Yoonjin

doi:10.1016/j.disc.2020.112159

Cited by 10 publications

(6 citation statements)

References 26 publications

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“…A DNA code can be identified with a code over F 4 = {0, 1, ω, ω 2 } by employing the standard bijective correspondence between F 4 and the DNA alphabet S D 4 = {A, T, C, G} given by η : F 4 → S D 4 , with η(0) = A, η(1) = T, η(ω) = C and η(ω 2 ) = G. The same correspondence has already been used in the literature, for example, please see [14]. We extend the bijection η so that η(C) is regarded as a DNA code for some code C over F 4 .…”

Section: Linear Codes and Dna Codesmentioning

confidence: 99%

“…Some known methods for designing DNA codes that satisfy certain conditions include the study of reversible self-dual codes over GF (4) [14], the study of cyclic and extended cyclic constructions [1] or the study of linear constructions [12]. Recently in [8], linear codes derived from group ring elements are considered to construct reversible DNA codes that satisfy the Hamming distance, reverse, reverse-complement and the fixed GC-content constraints.…”

Section: Introductionmentioning

confidence: 99%

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Reversible $G^k$-Codes with Applications to DNA Codes

Korban¹,

Şahinkaya²,

Üstün³

2021

Preprint

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In this paper, we give a matrix construction method for designing DNA codes that come from group matrix rings. We show that with our construction one can obtain reversible G k -codes of length kn, where k, n ∈ N, over the finite commutative Frobenius ring R. We employ our construction method to obtain many DNA codes over F 4 that satisfy the Hamming distance, reverse, reverse-complement and the fixed GCcontent constraints. Moreover, we improve many lower bounds on the sizes of some known DNA codes and we also give new lower bounds on the sizes of some DNA codes of lengths 48, 56, 60, 64 and 72 for some fixed values of the Hamming distance d.

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Section: Linear Codes and Dna Codesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Reversible $G^k$-Codes with Applications to DNA Codes

Korban¹,

Şahinkaya²,

Üstün³

2021

Preprint

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“…Siap et al [22] identified the four symbols A, C, G, T with the elements in R, and constructed cyclic DNA codes considering the GC-content(GC-weight) constraint over R and used the deletion distance. Our previous papers [5], [15] also introduced efficient and feasible algorithms for designing DNA codes from reversible self-dual codes over the finite field GF (4). We could point out that our algorithms take advantage of the reversibility and selfduality of reversible self-dual codes over GF (4) in [5], [15].…”

Section: Introductionmentioning

confidence: 99%

“…Our previous papers [5], [15] also introduced efficient and feasible algorithms for designing DNA codes from reversible self-dual codes over the finite field GF (4). We could point out that our algorithms take advantage of the reversibility and selfduality of reversible self-dual codes over GF (4) in [5], [15]. We expect similar algorithms for designing DNA codes to apply to reversible self-dual codes over the ring F 2 + uF 2 as well.…”

Section: Introductionmentioning

confidence: 99%

Reversible Self-Dual Codes Over the Ring F₂ + uF₂

Kim,

Choi

2024

IEEE Access

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In this study, we introduce bisymmetric self-dual codes over the finite field F 2 of order two. We developed a method to generate binary bisymmetric self-dual codes from a small-length bisymmetric self-dual code by increasing its length. Using this method, we produced binary bisymmetric self-dual codes and discovered that numerous such codes exhibit favorable parameters. Also, we defined the map from binary bisymmetric self-dual codes to reversible self-dual codes over the ring F 2 + uF 2 . This implies that there exists a one-toone correspondence between the bisymmetric code over F 2 and the reversible self-dual code over F 2 + uF 2 . Consequently, using this map on generated bisymmetric self-dual codes, we obtained reversible self-dual codes over F 2 + uF 2 , which were difficult to obtain using previously known methods.INDEX TERMS code over a ring, reversible self-dual code, eigenvectors, bisymmetric matrix, bisymmetric self-dual codes

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“…⟨0, 3, 4, 7, 10, 11, 14⟩, 1,4 = ⟨1, 2, 6, 7, 10, 12, 14⟩, 2,2 = ⟨0, 1⟩, 2,3 = ⟨1, 4, 5, 9, 10, 15⟩, 2,4 = ⟨0, 3, 4, 7, 8, 9, 12, 14⟩, 3,3 = 3,4 = ⟨0, 1, 2,3,4,5,6,7,8,9,10,11,12,13,14,15, 16⟩, ⟨0⟨0, 1⟩, 1,4 = 2,5 = ⟨1, 4⟩, 1,5 = 2,4 = ⟨1, 2, 3, 4⟩, ⟨0⟨2, 4⟩, 1,5 = 4,4 = 4,6 = ⟨0, 1, 2, 3, 4, 5⟩, 1,6 = ⟨0, 1, 3, 5⟩, 2,4 = ⟨3⟩, 2,6 = ⟨0, 1, 2, 4, 5⟩, 3,3 = ⟨0, 1⟩, 3,4 = ⟨0, 3, 4⟩, 3,5 = ⟨3, 4⟩, 3,6 = ⟨0, 2, 5⟩, ⟨0⟨1, 4⟩, 2,5 = ⟨0, 1, 4, 5⟩, 2,6 = 3,6 = 4,4 = 4,6 = ⟨0, 1, 2, 3, 4, 5⟩, 2,7 = ⟨1⟩, 3,3 = ⟨0, 2, 4⟩, 3,7 = ⟨1, 3, 5⟩, ⟨0⟨0, 2, 4⟩, 1,6 = 2,5 = 3,8 = 4,7 = ⟨0, 1, 4⟩, 1,7 = 2,8 = ⟨0, 2⟩, 1,8 = ⟨1, 2, 4⟩, 2,6 = 3,7 = ⟨3⟩, 2,7 = ⟨2⟩, 3,5 = 4,6 = ⟨1⟩, 3,6 = ⟨1, 4⟩, 4,5 = ⟨1, 2, 3, 4⟩, 5,5 = 6,6 = 7,7 = 8,8 = ⟨0, 5⟩954 24 121,1 = 1,2 = 3,3 = 3,4 = ⟨0⟩, 1,6 = ⟨1⟩, 1,7 = ⟨1, 3, 5⟩, 1,8 = ⟨0, 2⟩, 1,9 = 2,5 = 3,5 = 4,5 = ⟨1, 2,4, 5⟩, 2,2 = 4,4 = ⟨0, 1⟩, 2,6 = 4,8 = ⟨0, 1, 4⟩, 2,7 = ⟨0, 1, 2, 3, 4⟩, 2,8 = ⟨1, 4⟩, 2,9 = ⟨0, 2, 3, 4⟩, 3,6 = ⟨3, 4⟩, 3,7 = ⟨0, 1, 3, 5⟩, 3,8 = ⟨2⟩, 3,9 = ⟨2, 3, 5⟩, 4,6 = ⟨0, 1, 2, 3⟩, 4,7 = ⟨0, 1, 2, 5⟩, 4,9 = ⟨0, 2, 4⟩, 5,5 = 7,7 = 9,9 = ⟨0, 6⟩, 6,6 = 6,7 = 8,8 = 8,9 = ⟨0, 1, 2, 3,…”

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