Publication 2007 Issue No. 10 - October Abstract - Mixed-Radix Gray Codes in Lee Metric
Mixed-Radix Gray Codes in Lee Metric
October 2007 (vol. 56 no. 10)
pp. 1297-1307
 ASCII Text x Madhusudhanan Anantha, Bella Bose, Bader AlBdaiwi, "Mixed-Radix Gray Codes in Lee Metric," IEEE Transactions on Computers, vol. 56, no. 10, pp. 1297-1307, October, 2007.
 BibTex x @article{ 10.1109/TC.2007.1083,author = {Madhusudhanan Anantha and Bella Bose and Bader AlBdaiwi},title = {Mixed-Radix Gray Codes in Lee Metric},journal ={IEEE Transactions on Computers},volume = {56},number = {10},issn = {0018-9340},year = {2007},pages = {1297-1307},doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2007.1083},publisher = {IEEE Computer Society},address = {Los Alamitos, CA, USA},}
 RefWorks Procite/RefMan/Endnote x TY - JOURJO - IEEE Transactions on ComputersTI - Mixed-Radix Gray Codes in Lee MetricIS - 10SN - 0018-9340SP1297EP1307EPD - 1297-1307A1 - Madhusudhanan Anantha, A1 - Bella Bose, A1 - Bader AlBdaiwi, PY - 2007KW - Lee DistanceKW - Gray CodeKW - Hamiltonian CycleKW - Toroidal NetworksVL - 56JA - IEEE Transactions on ComputersER -
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.

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Index Terms:
Lee Distance, Gray Code, Hamiltonian Cycle, Toroidal Networks
Citation:
Madhusudhanan Anantha, Bella Bose, Bader AlBdaiwi, "Mixed-Radix Gray Codes in Lee Metric," IEEE Transactions on Computers, vol. 56, no. 10, pp. 1297-1307, Oct. 2007, doi:10.1109/TC.2007.1083