A theoretical study of complementary binary code sequences and a computer search for new kernels.

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Author
Jauregui, Stephen Jr.
Date
1962-05Advisor
Klamm, C.F. Jr.
Second Reader
Gray, Glenn A.
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Show full item recordAbstract
Complementary binary sequences were invented by Golay in an investigation
of infra-red multi-slit spectrometry. This dissertation
formalizes the basic results obtained by Golay and develops new concepts
and techniques for examining the characteristics of these special binary
codes. This work has developed new understanding of the structure and
methods for the decomposition of complementary sequences.
Complementary sequences have the property of an infinite correlation
peak to ambiguity ratio when detected with a matched filter. These
binary sequences should find much application as pseudo- random noise
modulation signals for both radar and communications systems.
A discussion of the need for such sequences is included in the introduction
and is followed by a state of the art description. An operations
group on the sequences is formulated and the proofs of several theorems
concerning the operations group are given in a rigorous manner. One
reason for developing the operations group is the application to elimination
of redundance in the computer search for new codes.
Several invariant properties of complementary codes are proved
through the use of the Hamming distance concept. Many more invariant
properties of the sequences are demonstrated through the introduction of
a Hamming vector. The concept of a Hamming vector is extremely useful
as a complementary code decomposition tool. A large number of
theorems are proved to enhance its use in this field.
Several computer searches for complementary sequences are
described and the actual computer programs for the CDC 1604 are included
in the Appendix.
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.Collections
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