  The first linear programming bound of McEliece, Rodemich, Rumsey, and Welch
is the best known asymptotic upper bound for binary codes, for a certain
subrange of distances. Starting from the work of Friedman and Tillich, there
are, by now, some arguably easier and more direct arguments for this bound. We
show that this more recent line of argument runs into certain difficulties if
one tries to go beyond this bound (say, towards the second linear programming
bound of McEliece, Rodemich, Rumsey, and Welch).
