Derived matroids: Comparison between three different concepts of derived matroids

Abstract

In this thesis, we first define error-correcting codes and describe many of their basic properties. Then we proceed to describe how matroids are a useful tool to determine many basic properties of error-correcting codes. In the remaining half of the thesis, we study a more specific theme; derived matroids. We describe in detail three different constructions, one invented already in 1979 by Longyear, as well as two newer ones invented respectively by Oxley and wang, as well as Freij-Hollanti, Jurrius, and Kuznetsova. We illustrate their similarities and differences through examples and also sketch an application of derived matroids, in computer science.