The mathematics of circular codes

• Applicant: Professor Dr. Lutz Strüngmann
• Subject Area: Mathematics
• Term: from 2022 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 508790756

Circular codes have their origins in theoretical biology and automata theory. They can be seen as a weak version of the well-studied comma-free codes (codes that do not require a separation symbol) proposed by Crick in 1957 to solve the problem of detecting frame shifts during protein synthesis. Roughly speaking, a circular code X is a set of words such that each motif from X (a concatenation of wordsfrom X) allows the original (construction) frame to be retrieved, maintained and synchronised. Although circular codes have great potential for applications in signal processing and data storage, a solid mathematical theory is lacking. Based on our own and other preliminary work, in this project we aim to systematically study circular codes over general alphabets and of arbitrary word length. Using methods from combinatorics, graph theory and group theory, we look for classification theorems, growth functions and construction algorithms.

• DFG Programme: Research Grants