Quasi perfect codes in the cartesian product of some graphs

S. A. Mane; N. V. Shinde

paper

Quasi perfect codes in the cartesian product of some graphs

arXiv:2510.13613

Abstract

An important question in the study of quasi-perfect codes is whether such codes can be constructed for all possible lengths $n$ . In this paper, we address this question for specific values of $n$ . First, we investigate the existence of quasi-perfect codes in the Cartesian product of a graph $G$ and a path (or cycle), assuming that $G$ admits a perfect code. Second, we explore quasi-perfect codes in the Cartesian products of two or three cycles, $C_{m} □ C_{n}$ and $C_{m} □ C_{n} □ C_{l}$ , as well as in the Cartesian products of two or three paths, $P_{m} □ P_{n}$ and $P_{m} □ P_{n} □ P_{l}$ .

14 pages, 10 figures