Boolean complementary pairs

Simple item page
dc.contributor.authorGobin, Jared
dc.contributor.examiningcommitteeGunderson, David (Mathematics)
dc.contributor.examiningcommitteeLi, Ben (Computer Science)
dc.contributor.examiningcommitteePrymak, Andriy (Mathematics)
dc.contributor.supervisorCraigen, Robert
dc.date.accessioned2023-09-07T14:22:44Z
dc.date.available2023-09-07T14:22:44Z
dc.date.issued2023-08-22
dc.date.submitted2023-08-22T23:16:33Zen_US
dc.degree.disciplineMathematicsen_US
dc.degree.levelMaster of Science (M.Sc.)
dc.description.abstractGolay pairs (GPs) are pairs of (1,-1)-sequences with zero autocorrelation. GPs have numerous applications in engineering and mathematics such as in device synchronization, spectroscopy, and in the construction of Hadamard matrices. As a result, there is significant interest in understanding their mathematical structure. However, the structure of GPs appears to be very mysterious. Ternary complementary pairs (TCPs)—a generalization of GPs—are pairs of (0,1,-1)-sequences with zero autocorrelation. Similar to GPs, the structure of TCPs appears to be quite challenging. In order to gain insight into TCPs and GPs, Craigen introduced Boolean complementary pairs (BCPs), which are pairs of Z_2-sequences with zero autocorrelation. Craigen solved the structure of even-weight BCPs and with Woodford discovered a factorization involving 2x2 matrices in the odd-weight case. A review of Golay pairs, ternary complementary pairs, and Boolean complementary pairs is given. The odd-weight BCP factorization is extended to all pairs of Z_2-sequences with zero autocorrelation. Consequences of this extension are then established, including a connection to affixes.
dc.description.noteOctober 2023
dc.description.sponsorshipDavid Gunderson
dc.identifier.urihttp://hdl.handle.net/1993/37599
dc.language.isoeng
dc.rightsopen accessen_US
dc.subjectComplementary pairs of sequences
dc.titleBoolean complementary pairs
dc.typemaster thesisen_US
local.subject.manitobano
oaire.awardTitleUniversity of Manitoba Graduate Fellowship
project.funder.identifierhttps://doi.org/10.13039/100010318
project.funder.nameUniversity of Manitoba Faculty of Graduate Studies
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
Jared Gobin MSc Thesis.pdf
Size:
768.77 KB
Format:
Adobe Portable Document Format
Description:
Download
License bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
license.txt
Size:
770 B
Format:
Item-specific license agreed to upon submission
Description:
Download
Collections
FGS - Electronic Theses and Practica