Master's Thesis
Over the last two years I have been a student at the University of Bergen, Departement of Informatics. I have worked on my master's thesis on boolean functions, unitary transforms, and recursions. My supervisor is Matthew G. Parker I thank him for all his help.
Single dimensional periodic and aperiodic autocorrelation are well-known metrics on binary sequences. These metrics play a very important role in communication engineering, and also other areas. They provide a means of telling how "good" or "bad" a sequence is from a coding theoretical point of view. In general, sequences with well-distributed spectra are preferred, and a good distribution is indicated by a set of low-magnitude autocorrelation values.In this thesis I explore the natural multi-dimensional expansion of these metrics.
I present various sequences created from Boolean functions. The length of these sequences is exponential in relation to the number of Boolean terms, so they grow very fast. An obvious problem with such long sequences is to "measure" them exactly, bit by bit, as our computing power is limited. However we have found that our measures create recursive values as the sequences grow in size. This enables us to tell the values of even infinite sequences. A large part of this thesis is devoted to finding such recursions for different metrics and functions. We believe that the knowledge we gain from exploring the simple functions will be applicable towards designing functions and sequences that are "good" with respect to our metrics.
These pages is an electronic presentation and documentation of my work. For the complete understanding of my work I refer to the thesis, located under "Documents". There are also some other notes and documents important to my results.
Most of my efforts have been writing software to compute various properties of binary sequences. Some of my code is simple c code. The major part is C#, written in Visual Studio.NET. All the code I have written can be found under "Software".
June 2005
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