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

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Authors
Jauregui, Stephen Jr.
Subjects
Advisors
Klamm, C.F. Jr.
Date of Issue
1962-05
Date
May 1962
Publisher
Monterey, California: U.S. Naval Postgraduate School
Language
en_US
Abstract
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.
Type
Thesis
Description
Series/Report No
Department
Electronics
Other Units
Naval Postgraduate School (U.S.)
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Citation
Distribution Statement
Approved for public release; distribution is unlimited.
Rights
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.
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