Designs, Codes and Cryptography vol:28 issue:2 pages:201-222
In this paper the problem for improvement of the Delsarte bound for tau-designs is investigated. Two main results are presented. Firstly, necessary and sufficient conditions for improving the bound are proved. We define test functions with the property that they are negative if and only if the Delsarte bound D(M, tau) can be improved by linear programming. Then we investigate the infinite polynomial metric spaces and give exact intervals, when the Delsarte bound is not the best linear programming bound possible. Secondly, we derive a new bound for the infinite PMS. Analytical forms of the extremal polynomials of degree tau + 2 for non-antipodal PMS and of degree tau + 3 for antipodal PMS are given. The new bound is investigated in different asymptotical processes for infinite PMS. When tau and n grow simultaneously to infinity our bound is better than Delsarte bound.