Abstract: The exponential growth of data has created a high demand for novel solutions to increase efficiency in communication networks and the reliability of large-scale storage systems. Error correction is essential for the development of large-scale quantum computers, where algorithms require low error rates. This dissertation contains new constructions and decoding approaches for codes based on non-conventional polynomials to provide new coding solutions to the abovementioned applications.
Available online: TUM library, arXiv
Abstract: Post-quantum cryptography is of high interest in recent years since some algorithms based on quantum computing already threaten the security of classical public-key cryptosystems, such as RSA. The McEliece system with Goppa codes, which was proposed in 1970s, is the most famous code-based cryptosystem and still stays secure today. In this thesis, we present a collaborative decoding for interleaved Goppa codes (IGC) is presented. The collaborative decoding increases the decoding radius beyond half of the minimum distance. Moreover, we revisit the McEliece system and investigate some well-known existing attacks. A new variant of the McEliece system, IntMcEliece, using wild IGC, is proposed. Some instances of parameter selection and key size are given.
A list of my publications is also available on Google Scholar.
[4] Liu, H., Wei, H., Wachter-Zeh, A., & Schwartz, M. (2024). Linearized Reed-Solomon Codes with Support-Constrained Generator Matrix and Applications in Multi-Source Network Coding. IEEE Transactions on Information Theory.
[3] Liu, H., Polianskii, N., Vorobyev, I., & Wachter-Zeh, A. (2021). Almost affinely disjoint subspaces. Finite Fields and Their Applications, 75, 101879.
[2] Liu, H., Wei, H., Puchinger, S., Wachter-Zeh, A., & Schwartz, M. (2021). On the gap between scalar and vector solutions of generalized combination networks. IEEE Transactions on Information Theory, 67(8), 5580-5591.
[1] Holzbaur, L., Liu, H., Neri, A., Puchinger, S., Rosenkilde, J., Sidorenko, V., & Wachter-Zeh, A. (2021). Decoding of interleaved alternant codes. IEEE Transactions on Information Theory, 67(12), 8016-8033.
[3] Ott, C., Liu, H., & Wachter-Zeh, A. (2023, February). Geometrical properties of balls in sum-rank metric. In WSA & SCC 2023; 26th International ITG Workshop on Smart Antennas and 13th Conference on Systems, Communications, and Coding (pp. 1-6). VDE.
[2] Ott, C., Liu, H., & Wachter-Zeh, A. (2022, September). Covering properties of sum-rank metric codes. In 2022 58th Annual Allerton Conference on Communication, Control, and Computing (Allerton) (pp. 1-7). IEEE.
[1] Huang, C. C., Liu, H., Holzbaur, L., Puchinger, S., & Wachter-Zeh, A. (2022, June). List decoding of 2-interleaved binary alternant codes. In 2022 IEEE International Symposium on Information Theory (ISIT) (pp. 2338-2343). IEEE.
[4] Couvée, H. S., & Liu, H. (2023). Notes on the Sum-Rank Weight of a Matrix with Restricted Rank. arXiv preprint arXiv:2311.10159.
[3] Liu, H., Ott, C., & Ulmer, F. (2023). A Gröbner Approach to Dual-Containing (θ, δ) -Codes over Finite Commutative Frobenius Rings. arXiv preprint arXiv:2308.13395.
[2] Liu, H., Holzbaur, L., Polyanskii, N., Puchinger, S., & Wachter-Zeh, A. (2021). Quadratic-curve-lifted Reed-Solomon codes. arXiv preprint arXiv:2109.14478.
[1] Liu, H., Holzbaur, L., & Wachter-Zeh, A. (2018). Locality in Crisscross Error Correction. arXiv preprint arXiv:1806.07496.