Quasi perfect codes in the cartesian product of some graphs
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918161166630912 |
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| author | Mane, S. A. Shinde, N. V. |
| author_facet | Mane, S. A. Shinde, N. V. |
| contents | 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, $C_m\square C_n$ and $C_m\square C_n\square C_l$, as well as in the Cartesian products of two or three paths, $P_m\square P_n$ and $P_m\square P_n\square P_l$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_13613 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quasi perfect codes in the cartesian product of some graphs Mane, S. A. Shinde, N. V. Combinatorics 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, $C_m\square C_n$ and $C_m\square C_n\square C_l$, as well as in the Cartesian products of two or three paths, $P_m\square P_n$ and $P_m\square P_n\square P_l$. |
| title | Quasi perfect codes in the cartesian product of some graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2510.13613 |