On the optimum of Delsarte's linear program
The author studies Delsarte's linear programming approach, which was used by \textit{R. McEliece, E. Rodemich, H. Rumsey}, and \textit{L. Welch} [IEEE Trans. Inf. Theory 23, 157--166 (1977; Zbl 0361.94016)] to get an upper bound for the size of error-correcting codes. The question is whether an even better upper bound can be derived using Delsarte's inequalities. The author arrives at a lower bound for what can be derived; this bound strictly exceeds the Gilbert-Varshamov bound and is at least as big as the average of the Gilbert-Varshamov bound and the McEliece-Rodemich-Rumsey-Welch bound. (In addition to unrestricted binary codes, constant weight codes are also considered in a similar vein.) NEWLINENEWLINENEWLINEOn the other hand, as the author also points out in a note added in proof, recent numerical results by \textit{A. Barg} and \textit{D. Jaffe} [in: Codes and association schemes, DIMACS, Ser. Discrete Math. Theor. Comput. Sci. 56, 25--32 (2001; Zbl 0989.94035)] indicate that the McEliece-Rodemich-Rumsey-Welch bound gives (asymptotically) the right answer to Delsarte's linear programming problem, which is not in accordance with the (probably incorrect) main conjecture of the current paper.
scientific article; zbMATH DE number 1694169