Date of Award
5-2025
Document Type
Thesis
Degree Name
Master of Arts in Mathematics
Department
Mathematics
First Reader/Committee Chair
Kim, Youngsu
Abstract
Codes and technology are part of our daily lives and allow the modern world to function, and for us to have conveniences in our lives such as smartphones that can be used to privately call people on the other side of the planet, and for secure access to the internet. In this thesis we will explore the construction of binary codes created by vertex-edge incidence matrices of planar graphs. The Hamming (7,4) code was an incredible code that allowed the detection and correction of errors after receiving them through a transmission. We will explore the possibility of the creation of generator matrices that can detect and possibly correct errors that occur due to interference caused between the message being sent and it being received. Here, we will provide a proof for tree and cycle graphs, as well as a basis for other graphs and future work.
Recommended Citation
Avalos, Joshua, "CONSTRUCTING BINARY ENCODING MATRICES FROM JOINED GRAPHS" (2025). Electronic Theses, Projects, and Dissertations. 2239.
https://scholarworks.lib.csusb.edu/etd/2239