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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| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/55058 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | 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. |
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