Equitable facto rtzations of Hamming shells *

We construct a l-factorizalion of the complement .E, of the linear Hamming code of length m:m,--2'-l in the z-cube Q^, for r ) 2,havitg the following equitable property: its component l-factors intersect each Cayley parallel l-factor of Q^ at a constant number of edges, (namely 2mr-r-t edges). In the way to that construction, we flnd an equitable m,-t-factorization of 2, formed by two factors Q,,Q',, speciflcally two spanning regular subgraphs, self-complementary in .E,. These results were already known for r ( 3, where fu and Q! coincide with the so-called Foster graph. @ 2002 Elsevier Science B.V. A11 rights reserved.