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Covering schemes of strength t

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Abstract

This work brings together several types of combinatorial designs: difference matrices, difference covering arrays and difference schemes by defining the concept of covering scheme of strength t over an abelian additive group. Connections of covering schemes with orthogonal arrays and covering arrays are also established. We show general results of covering schemes of strength t using a method based on the factorization of a group and some refinements for particular classes. We apply the previous results to investigate covering schemes having three, four and five factors. Finally, a reformulation of covering schemes in terms of graph theory is established.

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Acknowledgements

The authors would like to thank the anonymous referees for their suggestions that significantly improved this paper.

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Authors and Affiliations

  1. Departamento Acadêmico de Matemática, Universidade Tecnológica Federal do Paraná, Via do Conhecimento, Km 1, Pato Branco, Paraná, 85503-390, Brazil

    André Guerino Castoldi

  2. Colegiado de Matemática, Universidade Estadual do Paraná, Av. Gabriel Experidião, Paranavaí, Paraná, 87703-000, Brazil

    Anderson Novaes Martinhão

  3. Departamento de Matemática, Universidade Estadual de Maringá, Av. Colombo, 5790, Maringá, Paraná, 87020-900, Brazil

    Emerson L. Monte Carmelo

  4. Colegiado de Matemática, Universidade Estadual de Mato Grosso do Sul, Cidade Universitária de Dourados, 351, Dourados, Mato Grosso do Sul, 79804-970, Brazil

    Otávio J. N. T. N. dos Santos

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  1. André Guerino Castoldi
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  2. Anderson Novaes Martinhão
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  3. Emerson L. Monte Carmelo
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  4. Otávio J. N. T. N. dos Santos
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Correspondence to Emerson L. Monte Carmelo.

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Communicated by M. Buratti.

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Castoldi, A.G., Martinhão, A.N., Monte Carmelo, E.L. et al. Covering schemes of strength t. Des. Codes Cryptogr. 91, 3563–3580 (2023). https://doi.org/10.1007/s10623-023-01252-2

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  • DOI: https://doi.org/10.1007/s10623-023-01252-2

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