Abstract
We present two new families of resolvable block designs. We introduce the notion of a weakly resolvable block design and prove the equivalence of such designs and nonbinary codes meeting the Johnson bound. We construct a new family of such codes.
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Funding
The research was carried out at the Kharkevich Institute for Information Transmission Problems of the Russian Academy of Sciences and was supported by the Russian foundation for Basic Research, project no. 19-01-00364, and the Bulgarian National Science Fund, grant no. 20-51-18002.
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Translated from Problemy Peredachi Informatsii, 2022, Vol. 58, No. 1, pp. 3–15 https://doi.org/10.31857/S0555292322010016.
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Bassalygo, L., Zinoviev, V. & Lebedev, V. Weakly Resolvable Block Designs and Nonbinary Codes Meeting the Johnson Bound. Probl Inf Transm 58, 1–12 (2022). https://doi.org/10.1134/S003294602201001X
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DOI: https://doi.org/10.1134/S003294602201001X