Dan Zhang

Dan Zhang

Ph.D. started in: 2017
Expected year of graduation: 2021
COINS consortium member: University of Bergen
Supervised by: Matthew Geoffrey Parker
Research area: Cryptography
Project title: Self-dual quantum codes
Project description: The objective of this project is to extend the approaches of classical error-correcting codes to quantum error-correcting codes and derive new quantum error-correcting codes. Zero-dimensional quantum stabilizer codes can be represented as self-dual additive codes over GF(4). A self-dual additive code over GF(4) can be represented by a simple undirected graph. This allows us to use concepts and algorithms from graph theory to characterise the graphs corresponding to strong codes. Two well-known self-dual quantum codes, Hexacode and the Dodecacode, correspond to regular graphs with a special nested structure. One important goal of this project is to find a construction technique for nested graph codes with a desirable distance. As mentioned before, linear codes with few weights have applications in strongly regular graphs. Constructing nested graph codes with a predictable distance based classic linear codes m be a prospective method. A code of this type can also be represented by quadratic Boolean functions. Boolean functions are a hot topic in cryptography because of their application in S-boxes in block cipher. The study of the relationship between Boolean functions and quantum codes is also an interesting topic of this project.