TARU PUBLICATIONS
Journal of Information and Optimization Sciences cover
Hybrid ·Peer-reviewed·ISSN (Online): 2169-0103·ISSN (Print): 0252-2667

WoS  JIF 2026 : 0.4 (Q4)

Powered by:Powered by

Monthly Journal: Publishes theoretical and applied research on topics in information and optimization sciences.

Issues up to 2022 co-published with and available at:Taylor & Francis
submissions@tarupublications.com
Open Access Research Article

On the covering radius of DNA repetition codes in R

*

* Corresponding author · click or hover a name for details

pp. 977–988Vol. 47Issue 3March 2026DOI: 10.47974/JIOS-1779XML
Received:
03 Jan 2024
Published Online:
15 Jul 2025
Article type:
Research Article
Language:
EN
Article no.:
JIOS-1779
Pages:
977–988

Abstract

In this correspondent, obtain to bounds of covering radius of DNA codes in R = ℤ2 + vℤ2, v2 = v by using different distance. Construct of various Repetition DNA codes and its covering radius of codes, Simplex Repetition DNA code for Unit Type and Zero divisor Type and finally MacDonald Repetition DNA codes of both type over R are determined. 

Keywords

Subject Classifications

11T7111T3068P3094B05

References

[1] M. L. Adleman, “Molecular computation of solutions to combinatorial problems,” Science, vol. 266, pp. 1021-1024 (1994).
[2] T. Aoki, P. Gaborit, M. Harada and M. Ozeki P. Sol’e, On the covering radius of Z4 codes and their lattices, IEEE Trans. Inform. Theory, Vol. 45, no. 6, pp. 2162-2168 (1999).
[3] C. Bachoc, Application of coding theory to the construction of modular lattices, Journal of Combin. Theory Ser., A78, 92-119 (1997).
[4] M. C. Bhandari, M. K. Gupta, A. K. Lal, and A. K., “On Z4 Simplex codes and their gray images,” Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-13, Lecture Notes in Computer Science, vol. 1719, pp. 170-180 (1999).
[5] A. Bonnecaze, P. Sol’e, C. Bachoc and B. Mourrain, Type II codes over Z4, IEEE Trans. Inform. Theory, Vol. 43, pp. 969-976 (1997).
[6] P. C. Pandian, “On covering radius of some codes over R = ℤ2 + uℤ2, where, u2 = 0, “ International Journal of Research in Applied, Natural and Social Sciences, vol. 2, no. 1, pp. 61–70, 2014.
[7] P. Chella Pandian, On covering radius of codes over R = ℤ2 + uℤ2, where, u2 = 0 using chinese euclidean distance, Journal of Discrete Mathematics, Algorithms and Applications Vol. 9, no. 2, pp. 1750017(1-8) (2017).
[8] P. Chella Pandian, On Covering Radius of Codes Over R = ℤ2 + uℤ2, where u2 = 0 Using Bachoc Distance, International Journal of Mathematics And its Applications, Vol. 5, no.4-C , pp. 277-282 (2017).
[9] P. Chella Pandian, On codes over ℤ23 and its covering radius for Lee weight and Homogeneous weight, Journal of Information and Optimization Sciences, Vol. 39, no.8 , pp. 1705-1715 (2018).
[10] P. Chella Pandian, Bounds on the covering radius of some classes of codes over R, Open Journal of Discrete Applied Mathematics, Vol. 2, no. 1, pp. 14-23 (2019).
[11] P. Chella Pandian, On the Covering Radius of DNA Code Over N, Asian Journal of Mathematical Sciences, Vol. 7, no. 2, pp.97-104 (2023).
[12] P. Chella Pandian , On the Covering Radius of DNA Code over a Finite Ring, Journal of Discrete Mathematics and Its Applications, Vol. 8, No. 2, pp. 75-82 (2023).
[13] G. D. Cohen, M. G. Karpovsky, H. F. Mattson,, J. R. Schatz, Covering radius- Survey and recent results, IEEE Trans. Inform. Theory, Vol. 31, no. 3, pp. 328-343 (1985).
[14] C. Cohen, A. Lobstein, N. J. A. Sloane, Further Results on the Covering Radius of codes, IEEE Trans. Inform. Theory, Vol. 32, no. 5, pp. 680-694 (1986).
[15] C. J. Colbourn, M. K. Gupta, On quaternary MacDonald codes, Proc. Information Technology:Coding and Computing (ITCC), pp. 212-215 (April 2003).
[16] I. Constantinescu, T. Heise, A metric for codes over residue class rings of integers, Problemy Peredachi Informatsii, Vol. 33, pp. 22-28 (1997).
[17] J. H. Conway and N. J. A. Sloane, “Self-dual codes over the integers modulo 4,” Journal of Combinatorial Theory Series A, vol. 62, pp. 30-45 (1993).
[18] S. Dodunekov and J. Simonis, “Codes and projective multisets,” The Electronic Journal of Communications, vol. 5, R37 (1998).
[19] S. T. Dougherty, M. Harada, and P. Solé, “Shadow codes over Z4 finite fields and their applications,” vol. 7, no. 4, pp. 507-529 (2001).
[20] C. Durairajan, On Covering Codes and Covering Radius of Some Optimal Codes, Ph. D. Thesis, Department of Mathematics, IIT Kanpur (1996).
[21] M. K. Gupta, D. G. Glynn, and T. A. Gulliver, “On Senary Simplex Codes,” Lecture Notes in Computer Science, pp. 112-121 (2001).
[22] M. K. Gupta and C. Durairajan, “On the Covering Radius of some Modular Codes,” Journal of Advances in Mathematics of Computations, vol. 8, no. 2, pp. 9 (2014).
[23] A. R. Hammons, P. V. Kumar, A. R. Calderbank, N. J. A. Sloane and P. Sol’e, The Z4-linearity of kerdock, preparata, goethals, and related codes. IEEE Trans. Inform. Theory, Vol. 40, pp. 301-319 (1994).
[24] M. Harada, New extremal Type II codes over Z4. Des. Codes and Cryptogr. Vol. 13, pp. 271-284 (1998).
[25] D. J. Watson, C. H. F. Crick, A structure for deoxyribose nucleic acid, Nature, Vol. 25, pp. 737-738 (1953).

Views: 113Downloads: 74Citations: 0