3-phase Golay triads

Author: 
Date created: 
2010-12-03
Identifier: 
etd6322
Keywords: 
Golay sequence
3-phase
Construction
Triad
Existence
Autocorrelation
Abstract: 

Golay triads were introduced by Frank in 1980, but have since been largely overlooked. This thesis gives the first complete counts of 3-phase Golay sequence triads of length at most 22. The counts are obtained by exhaustive search, based on properties of Golay sequences used in multicarrier transmission. The existence pattern revealed is surprisingly rich, and leads to the conjecture: there are no 3-phase Golay sequence triads of length congruent to 4 modulo 6.This thesis also studies the structure of 3-phase Golay sequence triads. Four transformations are defined that induce an equivalence relation on the set of 3-phase Golay sequence triads of a given length. Moreover, a construction for Golay sequence triads due to Frank is generalized to multiple dimensions. This generalization is part of a four-stage construction process that accounts for many of the known 3-phase Golay sequence triads of length 3n.

Document type: 
Thesis
Rights: 
Copyright remains with the author. The author granted permission for the file to be printed and for the text to be copied and pasted.
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Senior supervisor: 
Jonathan Jedwab
Department: 
Science: Department of Mathematics
Thesis type: 
(Thesis) M.Sc.
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