Mixed-Radix Gray Codes in Lee Metric

TitleMixed-Radix Gray Codes in Lee Metric
Publication TypeJournal Article
Year of Publication2007
AuthorsAnantha, M., B. Bose, and B. F. AlBdaiwi
JournalIEEE Transactions on Computers
Volume56
Issue10
Pagination1297 - 1307
Date Published10/2007
ISSN0018-9340
KeywordsGray codes, Hamiltonian cycles, lee distance, toroidal networks
Abstract

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, kappa, 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 = 2r for some r ges 0. Efficient algorithms for the generation of these codes are then shown.

DOI10.1109/TC.2007.1083
Short TitleIEEE Trans. Comput.