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| Let be the minimum size of a code over of length n, constant weight w, such that every word with weight t is within Hamming distance d of at least one codeword. In this paper, we determine for all n≥4, q=3, 4 or q= +1 with m≥2, leaving the only case (q,n)=(3,5) in doubt. Our construction method is mainly based on the auxiliary designs, H-frames, which play a crucial role in the recursive constructions of group divisible 3-designs similar to that of candelabra systems in the constructions of 3-wise balanced designs. |
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| Keywords:Combinatorics; Constant weight covering codes; group divisible t-covering; group divisible t-design; H-frame |
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