Steiner systems

Bachelor thesis (2024)

Authors

G.N. Briejer Electrical Engineering, Mathematics and Computer Science

Contributors

J.G. Spandaw Analysis - EEMCS (mentor)
Dion Gijswijt Discrete Mathematics and Optimization - EEMCS (graduation committee member)
Faculty
Electrical Engineering, Mathematics and Computer Science
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Published Date

18-07-2024

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

One of the main focuses of this thesis is a special kind of symmetrical arrangement called a "Steiner system." Imagine trying to organize a group of objects in such a way that every possible subset of them fits together in a very specific and symmetrical pattern. These patterns are not just mathematical coincidences; they have real-world applications, such as in coding theory.

More precisely, among these Steiner systems, there are some particularly interesting ones known as "Witt designs." These designs are important because their symmetrical properties are used in constructing certain types of error-correcting codes. These codes can correct a certain amount of errors within information that is sent or stored, making it more reliable.

To better understand these Witt designs, the thesis explores two main ways to create them. One method uses something called the Golay code, which is a specific type of error-correcting code. The other method involves a mathematical group called the projective special linear group. Both of these constructions are explained in detail, with proofs provided to show that they indeed form the desired symmetrical patterns.

Files

Steiner_systems_3_.pdf
(pdf | 0.396 Mb)
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