  The rate vs. distance problem is a long-standing open problem in coding
theory. Recent papers have suggested a new way to tackle this problem by
appealing to a new hierarchy of linear programs. If one can find good dual
solutions to these LPs, this would result in improved upper bounds for the rate
vs. distance problem of linear codes. In this work, we develop the first dual
feasible solutions to the LPs in this hierarchy. These match the best-known
bound for a wide range of parameters. Our hope is that this is a first step
towards better solutions, and improved upper bounds for the rate vs. distance
problem of linear codes.
