Graduate Thesis Or Dissertation
 

Gray codes and their applications

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/hd76s4515

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  • An n-bit Gray code is an ordered set of all 2n binary strings of length n. The special property of this listing is that Hamming distance between consecutive vectors is exactly 1. If the last and first codeword also have a Hamming distance 1 then the code is said to be cyclic. This dissertation addresses problems dealing with the design and applications of new and existing types of both binary and non-binary Gray codes. It is shown how properties of certain Gray codes can be used to solve problems arising in different domains. New types of Gray codes to solve specific types of problems are also designed. We construct Gray codes over higher integral radices and show their applications. Applications of new classes of Gray codes defined over residue classes of Gaussian integers are also shown. We also propose new classes of binary Gray codes and prove some important properties of these codes.
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