Issue No. 10 - October (2007 vol. 56)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TC.2007.1083
Gray codes, where two consecutive codewords differ in exactly one position by $\pm 1$,are given. In a single radix code, all dimensions have the same base, say $k$, whereas in a mixed radix code the base in one dimension can be different from the base in another dimension. Constructions of new classes of mixed radix Gray codes are presented. It is shown how these codes can be used as a basis for constructing edge disjoint Hamiltonian cycles in mixed radix toroidal networks when the number of dimensions, $n=2^r$ for some $r \geq 0$. Efficient algorithms for the generation of these codes are then shown.
Lee Distance, Gray Code, Hamiltonian Cycle, Toroidal Networks
M. Anantha, B. AlBdaiwi and B. Bose, "Mixed-Radix Gray Codes in Lee Metric," in IEEE Transactions on Computers, vol. 56, no. , pp. 1297-1307, 2007.