On a Pair of Dual Subschemes of the Hamming Scheme Hn(q)

We consider codes in the Hamming association scheme Hn (q) with interesting metric properties. We describe how a uniformly packed linear code C determines a pair of dual subschemes. The existence of this pair of sub schemes is used to establish restrictions on the possible distances between codewords in the dual code C.L. These restrictions also apply to arbitrary codes with degree e + 1 and strength 2e or 2e + 1. An analogous result gives necessary conditions for the existence of non-linear uniformly packed codes. When q = 2 we determine the possible parameters of uniformly packed 2-error-correcting linear codes.