Packing and decomposition problems for polynomial association schemes
European Journal of Combinatorics - Special issue: association schemes
On designs in compact metric spaces and a universal bound on their size
Proceedings of the conference on Discrete metric spaces
Handbook of Coding Theory
Improvement of the Delsarte Bound for &tgr;-Designs When It Is Not the Best Bound Possible
Designs, Codes and Cryptography
Krawtchouk polynomials and universal bounds for codes and designs in Hamming spaces
IEEE Transactions on Information Theory
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In this paper the problem for the improvement of the Delsarte bound for Τ-designs in finite polynomial metric spaces is investigated. First we distinguish the two cases of the Hamming and Johnson Q- polynomial metric spaces and give exact intervals, when the Delsarte bound is possible to be improved. Secondly, we derive new bounds for these cases. Analytical forms of the extremal polynomials of degree Τ + 2 for non-antipodal PMS and of degree Τ + 3 for antipodal PMS are given. The new bound is investigated in the following asymptotical process: in Hamming space when Τ and n grow simultaneously to infinity in a proportional manner and in Johnson space when Τ, w and n grow simultaneously to infinity in a proportional manner. In both cases, the new bound has better asymptotical behavior then the Delsarte bound.