On the Construction of Reversible Linear Codes over the Field F 2r
Year: 2026
Type: conference-paper
Abstract: In this paper, we present a systematic construction of a family of linear codes of length 2mover the finite field ${\mathbb{F}_{{2^r}}}$. We show that the constructed codes have parameters [2m,2m−m−1,4] for all m ≥ 2 and r ≥ 1. For the special cases r = 1 and r = 2, the obtained codes are shown to be optimal with respect to known upper bounds on the minimum distance. In addition, we prove that the constructed codes are reversible, and that the reverse-complement of every codeword also belong to the code. This reversibility property makes the constructed family particularly suitable for applications in DNA coding. The explicit algebraic nature of the construction provides a flexible framework for further extensions and applications.
Authors: Sujata Bansal, Pramod Kumar Kewat
Institution: Indian Institute of Technology Dhanbad
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W7204193892