Vira Hari Krisnawati, Ardi Nur Hidayat, Muhammad Husnul Khuluq
Binary linear codes play an essential role in communication systems by ensuring reliable data transmission. One approach to constructing binary linear codes is through graph theory. In this paper, we study the construction of binary linear codes derived from the incidence matrices of zero divisor graphs of the rings Z(pα) and Z(pα qβ), where p, q are prime numbers and α, β ≥ 1 are integers. We analyze the parameters of the resulting binary linear codes, such as their length, dimension, and minimum distance. Furthermore, we investigate some examples of the constructed codes. To justify their theoretical and practical relevance, we perform an optimality analysis comparing the constructed codes with classical bounds. All evaluated codes strictly satisfy the Hamming sphere-packing bound. This work offers a new contribution to the study of linear codes by combining ideas from algebra, graph theory, and coding theory. © 2026 The Authors.
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Brawijaya University, East Java, Malang, 65145, Indonesia; Department of Mathematics, Faculty of Mathematics and Natural Sciences, State University of Surabaya, East Java, Surabaya, 60231, Indonesia
Research at a Glance
Register to unlock
Topics & SDG Alignment
Register to unlock
Collaboration
Register to unlock
Author Profile (Selected)
Register to unlock
References Overview
Register to unlock
Journal & Source
Register to unlock
Metadata & Integrity
Register to unlock