Remark on balanced incomplete block designs, near-resolvable block designs, and q-ary constant-weight codes
We prove that any balanced incomplete block design B(v, k, 1) generates a nearresolvable balanced incomplete block design NRB(v, k − 1, k − 2). We establish a one-to-one correspondence between near-resolvable block designs NRB(v, k −1, k −2) and the subclass of nonbinary (optimal, equidistant) constant-weight codes meeting the generalized Johnson bound.
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- 4.Abel, R.J.R., Ge, G., and Yin, J., Resolvable and Near-Resolvable Designs, Sec. VI.7 of Handbook of Combinatorial Designs, Colbourn, C.J. and Dinitz, J.H., Eds., Boca Raton: Chapman & Hall, 2007, 2nd ed., pp. 124–132.Google Scholar