Graduation date: 2008
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.