Hamiltonicity ofMinimum Distance Graphsof 1-Perfect Codes

[摘要] A 1-perfect code $\mathcal{C}_{q}^{n}$ is called Hamiltonian if its minimum distance graph $G(\mathcal{C}_{q}^{n})$ contains a Hamiltonian cycle. In this paper, for  all admissible lengths $n \geq 13$, we construct   Hamiltonian nonlinear ternary 1-perfec

[学科分类] 离散数学和组合数学

[关键词] Hamiltonian cycle;minimum distance graph;Hamming code;nonlinear code;$q$-ary1-perfect code.