PhD defense by René Bødker Christensen


30.10.2020 kl. 13.00 - 16.00


Quantum Codes and Multiparty Computation: A Coding Theoretic Approach


This thesis treats the application of results and techniques from classical coding theory to protocols in cryptography and construction of quantum error-correcting codes. Specifically, secret sharing is a common building block in cryptographic protocols providing secure and private computation on sensitive data. Quantum error-correction is crucially important for large scale quantum computers, whose computational power promises to vastly surpass the classical computers known today.

It turns out that the study of nested (classical) code pairs leads to the construction of both secret sharing schemes and quantum error-correcting codes. In both cases, the codimension of the codes, their relative distance, and the relative distance of the duals determine the parameters of interest.

In this talk, we consider codes defined from the Hermitian function field, both the usual Hermitian codes and so-called order bound improved codes. These are generally known to have good parameters, and additionally the relative distances of the codes and their duals are relatively easy to describe. This makes them prime candidates for the constructions mentioned above. Choosing the nested code pairs strategically gives good parameters in both applications. The talk contains two such strategies. In addition, we consider a third nesting approach, which is applicable to the construction quantum codes via the so-called Steane-enlargement technique.

Assessment Committee:       

Professor Morten Nielsen (chairman)
Department of Mathematical Sciences, Aalborg University, Denmark

Professor Serge Fehr
Mathematical Institute Leiden University, The Netherlands

Cem Güneri, PhD,  Vice President, Sabanci University, Turkey

Professor Olav Geil, Department of Mathematical Sciences, Aalborg University

The PhD defense will be hosted by Moderator Martin Raussen. The lecture constitutes a 45 minutes presentation by René Bødker Christensen followed by a short break and a discussion session with questions from the opponents and the auditorium.





Department of Mathematical Sciences


Skjernvej 4A, AUD 5.034