**Project period: June 1, 2018 – July 31, 2021.**

The project consists of strengthening and extending an already existing co-operation between IIT-Bombay and UiT – The Arctic University of Norway, in the field of error-correcting codes. One develops further a useful mathematical theory for how to encode and represent digital information that is sent over some channel, such that the information signals that are vulnerable to noise and disturbances, become more robust when exposed to these disturbances.

The goal is to find methods, such that the receiver can receive and interpret the signals in a completely correct way, even if the signals are distorted (within limits).

Typical examples of information that is encoded and sent this way are TV pictures, and design of registration numbers. Coding theory can also be used as a tool within cryptological settings, where the users combine these methods with other techniques, where one encrypts information. The mathematical techniques that one uses are algebra, combinatorics, and algebraic geometry, which are well established and classical mathematical theories, which have proved to be extremely useful both in coding theory and many other areas, over the last decades.

During the project period (so far) the participants have published several within these themes in internationally recognized journals or lecture notes. In one of the published works one has contributed to show how one can increase the degree of freedom when choosing signal symbols that carry information. This is done without losing the good properties enjoyed while choosing signal symbols in a more restrictive way. This applies both to robustness regarding noise under transmission, and the quality of the mathematical tools when alternatively being used for tapping of signals (a bi-effect of the work). In other published articles one treats how one can find as many points as possible on various geometric objects (curves, surfaces aso.) One chooses these objects in an optimal way, such that they have a potential for construction of error-correcting codes that can represent as large amounts of information as possible.

In addition several other articles, which treat similar themes, have been submitted to similar journals for publication.