Programme: Recovery and Resilience Plan

One of the main problems in the field of digital technologies is related to the protection of information. Coding aims to protect information on communication channels and when it is stored on different media. A key parameter for error-correction and error-detection code is its coverage radius. It provides information about whether the code is suitable for use in data compression and anti-noise coding algorithms. It is also used in linear code generation and classification algorithms. The task of finding a covering radius is NP-complete, which makes it suitable for parallel implementation using high-performance systems (HPC). The main task of the current project is the development of a parallel implementation of an algorithm for calculating the covering radius of linear codes. The task consists of two basic components: learning methods for finding the covering radius and efficient use of modern high-performance computing techniques. One approach to finding the covering radius uses the column vectors of the code's parity-check matrix. The main computational resource for this method implements operations on vectors over finite fields. This makes it suitable for parallelization via extended vector registers that are available in modern CPUs. The developed HPC algorithms can be used to determine optimal codes with good coverage radius.