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 subschemes is used to establish restrictions on the possible distances between codewords in the dual code C⊥. 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. © 1985, Academic Press Inc. (London) Limited. All rights reserved.
Calderbank, AR; Goethals, JM
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