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Volume 14
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

On Double Cyclic Codes and Applications to DNA Codes

by
Amal S. Alali
1,
Mohd Anwar
2 and
Muzibur Rahman Mozumder
2,*
1
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
2
Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
*
Author to whom correspondence should be addressed.
Mathematics 2026, 14(1), 40; https://doi.org/10.3390/math14010040
Submission received: 27 November 2025 / Revised: 19 December 2025 / Accepted: 20 December 2025 / Published: 22 December 2025
(This article belongs to the Special Issue Mathematics for Algebraic Coding Theory and Cryptography)
Versions Notes

Abstract

In this paper, we investigate the structure of double cyclic codes of length (α,β) over R=F4+ϱF4,ϱ2=0 and give a minimal spanning set of double cyclic codes. Moreover, we extend this study to construct DNA codes from R-double cyclic codes. Furthermore, we explore reversible and reversible-complement double cyclic codes over R and present a necessary and sufficient condition for separable R-double cyclic codes to be reversible and reversible-complement R-double cyclic codes. Also, we study reversible and reversible-complement double cyclic codes over R for non-separable case and construct some optimal R-double cyclic codes, and several DNA codes to support our results.
Keywords: double cyclic code; reversible double cyclic codes; double cyclic DNA code; Watson–Crick complement rule double cyclic code; reversible double cyclic codes; double cyclic DNA code; Watson–Crick complement rule

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MDPI and ACS Style

Alali, A.S.; Anwar, M.; Mozumder, M.R. On Double Cyclic Codes and Applications to DNA Codes. Mathematics 2026, 14, 40. https://doi.org/10.3390/math14010040

AMA Style

Alali AS, Anwar M, Mozumder MR. On Double Cyclic Codes and Applications to DNA Codes. Mathematics. 2026; 14(1):40. https://doi.org/10.3390/math14010040

Chicago/Turabian Style

Alali, Amal S., Mohd Anwar, and Muzibur Rahman Mozumder. 2026. "On Double Cyclic Codes and Applications to DNA Codes" Mathematics 14, no. 1: 40. https://doi.org/10.3390/math14010040

APA Style

Alali, A. S., Anwar, M., & Mozumder, M. R. (2026). On Double Cyclic Codes and Applications to DNA Codes. Mathematics, 14(1), 40. https://doi.org/10.3390/math14010040

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