SavedAdd your journal

Journals / Journal of Algebra Combinatorics Discrete Structures and Applications / 2017 / Cilt: 4 - Sayı: 1

On DNA codes from a family of chain rings

Elif Segah Oztas
Bahattin Yildiz
Irfan Siap
Pages
93–102
Publication Date
2017-01-11
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We then conclude our study with some examples.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this work, we focus on reversible cyclic codes which correspond to reversible DNA codes or reversible-complement DNA codes over a family of finite chain rings, in an effort to extend what was done by Yildiz and Siap in \cite{YildizSiap}.
📊
Key Findings & Data:The ring family that we have considered are of size $2^{2^k}$, $k=1,2, \cdots$ and we match each ring element with a DNA $2^{k-1}$-mer.
💡
Conclusion & Impact:We then conclude our study with some examples.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Cyclic codes · Chain rings · Reversible codes

Abstract

In this work, we focus on reversible cyclic codes which correspond to reversible DNA codes or reversible-complement DNA codes over a family of finite chain rings, in an effort to extend what was done by Yildiz and Siap in \cite{YildizSiap}. The ring family that we have considered are of size $2^{2^k}$, $k=1,2, \cdots$ and we match each ring element with a DNA $2^{k-1}$-mer. We use the so-called $u^2$-adic digit system to solve the reversibility problem and we characterize cyclic codes that correspond to reversible-complement DNA-codes. We then conclude our study with some examples.

🔖

Cite This Article

Oztas, E. S., Yildiz, B., Siap, I. (2017). On DNA codes from a family of chain rings. Journal of Algebra Combinatorics Discrete Structures and Applications, Cilt: 4 - Sayı: 1, 93–102. https://ajindex.com/articles/861649

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (17)

  1. N. Aboluion, D. H. Smith, S. Perkins, Linear and nonlinear constructions of DNA codes with Hamming distance d, constant GC–content and a reverse–complement constraint, Discrete Math. 312(5) (2012) 1062–1075
  2. T. Abulraub, A. Ghrayeb, X. N. Zeng, Construction of cyclic codes over GF(4) for DNA computing, J. Frankl. Inst. 343(4–5) (2006) 448–457
  3. L. Adleman, Molecular computation of solutions to combinatorial problems, Science 266(5187) (1994) 1021–1024
  4. L. Adleman, P. W. K. Rothemund, S. Roweis, E. Winfree, On applying molecular computation to the Data Encryption Standard, J. Comput. Biol. 6(1) (1999) 53–63
  5. R. Alfaro, S. Bennett, J. Harvey, C. Thornburg, On distances and self–dual codes over Fq[u]=(ut), Involv. J. Math. 2(2) (2009) 177–194
  6. D. Boneh, C. Dunworth, R. Lipton, Breaking DES using molecular computer, Princeton CS Tech–Report, Number CS–TR-489–95, 1995
  7. A. G. Frutos, Q. Liu, A. J. Thiel, A. M. W. Sanner, A. E. Condon, L. M. Smith, R. M. Corn, Demonstration of a word design strategy for DNA computing on surfaces, Nucleic Acids Res. 25(23) (1997) 4748–4757
  8. P. Gaborit, O. D. King, Linear construction for DNA codes, Theoret. Comput. Sci. 334(1–3) (2005) 99–113
  9. O. D. King, Bounds for DNA codes with constant GC–content, Electron. J. Comb. 10 (2003) 1–13
  10. M. Li, H. J. Lee, A. E. Condon, R. M. Corn, DNA word design strategy for creating sets of non–interacting oligonucleotides for DNA microarrays, Langmuir 18(3) (2002) 805–812
  11. M. Mansuripur, P. K. Khulbe, S. M. Kuebler, J. W. Perry, M. S. Giridhar, N. Peyghambarian, Information storage and retrieval using acromolecules as storage media, in Optical Data Storage, OSA Technical Digest Series (Optical Society of America) paper TuC2, 2003
  12. A. Marathe, A. E. Condon, R. M. Corn, On combinatorial DNA word design, J. Comput. Biol. 8(3) (2001) 201–220
  13. J. L. Massey, Reversible codes, Inform. and Control 7(3) (1964) 369–380
  14. G. H. Norton, A. Salagean, On the structure of linear and cyclic codes over a finite chain ring, Appl. Algebr. Eng. Comm. 10 (2000) 489–506
  15. E. S. Oztas, I. Siap, Lifted polynomials Over F16 and their applications to DNA codes, Filomat 27(3) (2013) 459–466
  16. E. S. Oztas, I. Siap, B. Yildiz, Reversible codes and applications to DNA, Lect. Notes Comput. Sc. 8592 (2014) 124–128
  17. E. S. Oztas, I. Siap, On a generalization of lifted polynomials over finite fields and their applications to DNA codes, Int. J. Comput. Math. 92