T The CSG (Code,Scheme, Group) research group has been operating as a research group in the Faculty of Mathematics and Statistics of Isfahan University in Iran since 2017. The core focus that led to the formation of this research group is "permutation codes", situated at the intersection of coding theory and group theory. These codes are subsets of symmetric groups over a set of symbols, and they hold particular importance when they possess group structures. A crucial tool in this field is the theory of schemes, which is used to study the maximum number of codewords for such codes with a given minimum distance.
1. Reducing errors in data storage and retrieval on flash memory and DNA molecules: storing information in DNA molecules offers unparalleled information density, and has been proven to be feasible. Also, flash memory is a non-volatile technology that is both electrically programmable and electrically erasable. It incorporates a set of cells maintained at a set of levels of charge to encode information. Potential issues, such as charge leakage in flash memory or retrieval errors in DNA, can be managed and improved using permutation codes.