Dan Zhang

1

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.

Courses attended:
  1. IMT6003 COINS Summer School (NTNU), 3 ECTS, 2018
Events attended with COINS funding:
  1. School on Applied Cryptography and its Impact on Society, Innovation and Entrepreneurship , Malaga, Spain, 2019
  2. COINS Finse winter school, Finse, Norway, 2019
  3. COINS Finse winter school, Finse, Norway, 2018
  4. COINS summer school, Metochi, Greece, 2018
  5. COINS Ph.D student seminar, Longyearbyen, Svalbard, Norway, 2018
  6. BFA 2018 workshop , Loen, Norway, 2018
  7. NISK 2018, Longyearbyen, Svalbard, Norway, 2018
  8. Number theory and coding theory: Contemporary applications in security, Turku, Finland, 2018
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