@article {IOPORT.06045689,
    author       = {Romanov, Alexander Mikhailovich},
    title        = {Hamiltonicity of minimum distance graphs of 1-perfect codes.},
    year         = {2012},
    journal      = {The Electronic Journal of Combinatorics [electronic only]},
    volume       = {19},
    number       = {1},
    issn         = {1077-8926},
    pages        = {Research Paper P65, 6 p., electronic only},
    publisher    = {Prof. Andr\'e K\"undgen, Deptartment of Mathematics, California State University San Marcos, San Marcos, CA},
    abstract     = {Summary: A 1-perfect code $\cal{C}_{q}^{n}$ is called Hamiltonian if its minimum distance graph $G(\cal{C}_{q}^{n})$ contains a Hamiltonian cycle. In this paper, for all admissible lengths $n \geq 13$, we construct Hamiltonian nonlinear ternary 1-perfect codes, and for all admissible lengths $n \geq 21$, we construct Hamiltonian nonlinear quaternary 1-perfect codes. The existence of Hamiltonian nonlinear $q$-ary 1-perfect codes of length $N = qn + 1$ is reduced to the question of the existence of such codes of length $n$. Consequently, for $q = p^r$, where $p$ is prime, $r \geq 1$ there exist Hamiltonian nonlinear $q$-ary 1-perfect codes of length $n = (q ^{m} -1) / (q-1)$, $m \geq 2$. If $q =2, 3, 4$, then $ m \neq 2$. If $q =2$, then $ m \neq 3$.},
    identifier   = {06045689},
}