Abstract
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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15 October 2017
The acknowledgment (footnote to the title of the paper) should read as follows: The research was carried out at the Institute for Information Transmission Problems of the Russian Academy of Sciences at the expense of the Russian Science Foundation, project no. 14-50- 00150.
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Original Russian Text © L.A. Bassalygo, V.A. Zinoviev, 2017, published in Problemy Peredachi Informatsii, 2017, Vol. 53, No. 1, pp. 56–59.
Supported in part by the Russian Foundation for Basic Research, project no. 14-50-00150.
An erratum to this article is available at https://doi.org/10.1134/S0032946017030127.
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Bassalygo, L.A., Zinoviev, V.A. Remark on balanced incomplete block designs, near-resolvable block designs, and q-ary constant-weight codes. Probl Inf Transm 53, 51–54 (2017). https://doi.org/10.1134/S0032946017010045
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DOI: https://doi.org/10.1134/S0032946017010045