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).

翻译：McEliece、Rodemich、Rumsey和Welch提出的第一线性规划界是已知二进制码在特定距离子范围内的最佳渐近上界。从Friedman和Tillich的工作开始，目前已存在若干相对更简单且更直接的论证方法。我们证明，若试图突破该界（例如朝向McEliece、Rodemich、Rumsey和Welch的第二线性规划界推进），这一较新的论证方法将遭遇某些困难。