Mixed Radix Gray Codes and Edge Disjoint Hamiltonian Cycles in Toroidal Networks

Gray codes, where two consecutive codewords differ in exactly one position by plusmn1, 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 a
cyclic

mixed

radix

Gray

code
corresponds to a Hamiltonian cycle in a mixed radix toroidal graph. It is then 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 ges 0.