Equivalence of Delsarte's bounds for codes and designs in symmetric association schemes, and some applications
Delsarte introduced two extremum problems for the systems of \(p\)-numbers and \(q\)-numbers to obtain bounds on the sizes of codes and designs in association schemes. The purpose of this paper is to prove that the Delsarte bound for codes obtained with the help of either of these systems is equivalent to that for designs obtained by using the other system. This means, in particular, that the universal Delsarte bound of 1973 for designs is equivalent to the sphere packing bound for codes. A relationship between bounds for orthogonal arrays and block designs has also been obtained which gives new lower bounds on the size of orthogonal arrays with the help of those for block designs.
scientific article; zbMATH DE number 1322035
scientific article