Mathematics, Vol. 11, Pages 4732: DNA Code Design Based on the Cosets of Codes over Z4

Mathematics, Vol. 11, Pages 4732: DNA Code Design Based on the Cosets of Codes over Z4

Mathematics doi: 10.3390/math11234732

Authors: Adel N. Alahmadi Fatimah Anas Melibari Manish K. Gupta

DNA code design is a challenging problem, and it has received great attention in the literature due to its applications in DNA data storage, DNA origami, and DNA computing. The primary focus of this paper is in constructing new DNA codes using the cosets of linear codes over the ring Z4. The Hamming distance constraint, GC-content constraint, and homopolymers constraint are all considered. In this study, we consider the cosets of Simplex alpha code, Kerdock code, Preparata code, and Hadamard code. New DNA codes of lengths four, eight, sixteen, and thirty-two are constructed using a combination of an algebraic coding approach and a variable neighborhood search approach. In addition, good lower bounds for DNA codes that satisfy important constraints have been successfully established using Magma software V2.24-4 and Python 3.10 programming in our comprehensive methodology.