2025/10/15 by S. A. Mane, Mane, S. A., N. V. Shinde +1
Computer Science · Engineering · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2510.13613
openalex publication_date 2025/10/15 · openalex created_date 2025/10/17 · openalex updated_date 2026/07/28
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, Cm\square Cn and Cm\square Cn\square Cl, as well as in the Cartesian products of two or three paths, Pm\square Pn and Pm\square Pn\square Pl.