Abstract
In this paper, we describe a new type of DNA codes over two noncommutative rings E and F of order four with characteristic 2. Our DNA codes are based on quasi self-dual codes over E and F. Using quasi self-duality, we can describe fixed GC-content constraint weight distributions and reverse-complement constraint minimum distributions of those codes.
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References
Adleman, L.M.: Molecular computation of solutions to combinatorial problems. Science 266(5187), 1021–1024 (1994)
Alahmadi, A., Alkathiry, A., Altassan, A., Basaffar, W., Bonnecaze, A., Shoaib, H., Solé, P.: Type IV codes over a non-local non-unital ring. Proyecciones (Antofagasta). 39(4), 963–978 (2020)
Alahmadi A., Altassan A., Basaffar W., Bonnecaze A., Shoaib H., Solé P.: Type VI codes over a non-unital ring. to appear in J. Algebra Appl. Available from https://hal.archives-ouvertes.fr/hal-02433480/document
Alahmadi A., Altassan A., Basaffar W., Bonnecaze A., Shoaib H., Solé P.: Quasi Type IV codes over a non-unital ring. preprint available from https://hal.archives-ouvertes.fr/hal-02544399/document
Bennenni, N., Guenda, K., Mesnager, S.: New DNA cyclic codes over rings. Adv. Math. Commum. 11(1), 83–98 (2017)
Bouyukliev, I., Bouyuklieva, S., Gulliver, T.A., Ostergard, P.R.J.: Classification of optimal binary self-orthogonal codes. J. Comb. Math. Comb. Comput. 59, 33–87 (2006)
Fine, B.: Classification of finite rings of order \(p^2\). Math. Mag. 66(4), 248–252 (1993)
Gaborit, P., King, O.D.: Linear constructions for DNA codes. Theor. Comput. Sci. 334(1–3), 99–113 (2005)
Guenda, K., Gulliver, T.A.: Construction of cyclic codes over \(\mathbb{F}_2 + u \mathbb{F}_2\) for DNA computing. Appl. Algebra Eng. Commun. 24(6), 445–459 (2013)
Hou, X.-D.: On the number of inequivalent binary self-orthogonal codes. IEEE Trans. Inform. Theory. 53(7), 2459–2479 (2007)
J.-L. Kim’s CICAGO Lab website https://cicagolab.sogang.ac.kr/cicagolab/2656.html
King, O.D.: Bounds for DNA codes with constant GC-content. Electron. J. Comb. 10, R33 (2003)
Liang, J., Wang, L.: On cyclic DNA codes over \(\mathbb{F}_2 + u \mathbb{F}_2\). J. Comput. Appl. Math. 51(1–2), 81–91 (2016)
Limbachiya D., Rao B., Gupta M. K.: The art of DNA strings: sixteen years of DNA coding theory. arXiv:1607.00266.pdf
MacWilliams, F.S., Sloane, N.J.A.: The Theory of Error-Correcting Codes., vol. 16. Elsevier. (1977)
Milenkovic, O., Kashyap, N.: On the design of codes for DNA computing. Intern. Workshop on coding and cryptography 100–119,(2005)
Pless, V.: A classification of self-orthogonal codes over \(GF(2)\). Discr. Math. 3(1–3), 209–246 (1972)
Siap, I., Abualrub, T., Ghrayeb, A.: Cyclic DNA codes over the ring \(\mathbb{F}_2 [u]/(u^2-1)\) based on the deletion distance. J. Franklin Inst. 346(8), 731–740 (2009)
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Kim, JL., Ohk, D.E. DNA codes over two noncommutative rings of order four. J. Appl. Math. Comput. 68, 2015–2038 (2022). https://doi.org/10.1007/s12190-021-01598-7
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DOI: https://doi.org/10.1007/s12190-021-01598-7