Delsarte System

The Delsarte System is a mathematical method used in coding theory and combinatorics to analyze and bound the size of sets with specific distance properties, such as error-correcting codes and arrangements on spheres. It employs algebraic and harmonic analysis tools, particularly orthogonal polynomials and eigenvalue techniques, to derive limits on how large such sets can be while maintaining certain spacing or distance conditions. Essentially, it provides a systematic way to understand the maximum capacity of arrangements that meet particular geometric or combinatorial criteria, optimizing design and error correction strategies.