Abstract
Constructions for optimal multiply constant-weight codes (MCWCs) with total weight 5 and distance 8 are studied. The equivalence between a special class of MCWCs and generalized Howell designs (GHDs) is established. The existences of GHD $$\big (\frac{3n-3}{2},3n\big )$$ s and GHD $$\big (\frac{3n-5}{2},3n\big )$$ s are discussed. As corollaries, a large number of optimal MCWCs are obtained.
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