New Solutions to Delsarte's Dual Linear Programs

Understand

Understanding the maximum size of a code with a given minimum distance is a major question in computer science and discrete mathematics.

• The most fruitful approach for finding asymptotic bounds on such codes is by using Delsarte's theory of association schemes.
• With this approach, Delsarte constructs a linear program such that its maximum value is an upper bound on the maximum size of a code with a given minimum distance.
• Bounding this value can be done by finding solutions to the corresponding dual linear program.