Numerical Results on the Asymptotic Rate of Binary Codes

We compute upper bounds on the maximal size of a binary linear code of length n=1000, dimension k, and distance d. For each value of d, the bound is found by solving the Delsarte linear programming problem. Relaying on the results of the calculations, we discuss the known bounds on the size of codes and some recent conjectures made about them. The most important conclusion is that Delsarte's linear programming method is unlikely to yield major improvements of the known general upper bounds on the size of codes.