RELATIVE T-DESIGNS: RECENT RESULTS AND OPEN PROBLEMS
The purpose of this thesis is to survey the latest results and pose open problems regarding relative t-designs. Around 2010, Bannai introduced a discrete analogue of Euclidean t-designs, which turned out to be equivalent to relative t-designs defined by Delsarte back in 1977. In this thesis, we w...
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id-itb.:550582021-06-14T09:30:40ZRELATIVE T-DESIGNS: RECENT RESULTS AND OPEN PROBLEMS Christofen Tang, Hopein Indonesia Final Project Relative t-design, tight relative t-design, Fisher type lower bound, association scheme, P-polynomial association scheme, Q-polynomial association scheme, Hamming scheme, Johnson scheme. INSTITUT TEKNOLOGI BANDUNG https://digilib.itb.ac.id/gdl/view/55058 The purpose of this thesis is to survey the latest results and pose open problems regarding relative t-designs. Around 2010, Bannai introduced a discrete analogue of Euclidean t-designs, which turned out to be equivalent to relative t-designs defined by Delsarte back in 1977. In this thesis, we will show that a relative t-design can be interpreted as a three-step generalization of a combinatorial t-design. This thesis covers various topics related to relative t-designs, namely the definition of relative t-designs in P-polynomial and Q-polynomial association schemes, elementary properties of relative t-designs, Fisher type lower bounds, and tight relative t-designs. Moreover, an explicit example and a new condition for the nonexistence of tight relative 2-designs on two shells in binary Hamming schemes will be given. text |
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The purpose of this thesis is to survey the latest results and pose open problems
regarding relative t-designs. Around 2010, Bannai introduced a discrete analogue of
Euclidean t-designs, which turned out to be equivalent to relative t-designs defined
by Delsarte back in 1977. In this thesis, we will show that a relative t-design can be
interpreted as a three-step generalization of a combinatorial t-design.
This thesis covers various topics related to relative t-designs, namely the definition
of relative t-designs in P-polynomial and Q-polynomial association schemes,
elementary properties of relative t-designs, Fisher type lower bounds, and tight
relative t-designs. Moreover, an explicit example and a new condition for the
nonexistence of tight relative 2-designs on two shells in binary Hamming schemes
will be given. |
| format |
Final Project |
| author |
Christofen Tang, Hopein |
| spellingShingle |
Christofen Tang, Hopein RELATIVE T-DESIGNS: RECENT RESULTS AND OPEN PROBLEMS |
| author_facet |
Christofen Tang, Hopein |
| author_sort |
Christofen Tang, Hopein |
| title |
RELATIVE T-DESIGNS: RECENT RESULTS AND OPEN PROBLEMS |
| title_short |
RELATIVE T-DESIGNS: RECENT RESULTS AND OPEN PROBLEMS |
| title_full |
RELATIVE T-DESIGNS: RECENT RESULTS AND OPEN PROBLEMS |
| title_fullStr |
RELATIVE T-DESIGNS: RECENT RESULTS AND OPEN PROBLEMS |
| title_full_unstemmed |
RELATIVE T-DESIGNS: RECENT RESULTS AND OPEN PROBLEMS |
| title_sort |
relative t-designs: recent results and open problems |
| url |
https://digilib.itb.ac.id/gdl/view/55058 |
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1822929792447545344 |