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Common information, matroid representation, and secret sharing for matroid ports

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Abstract

Linear information and rank inequalities as, for instance, Ingleton inequality, are useful tools in information theory and matroid theory. Even though many such inequalities have been found, it seems that most of them remain undiscovered. Improved results have been obtained in recent works by using the properties from which they are derived instead of the inequalities themselves. We apply here this strategy to the classification of matroids according to their representations and to the search for bounds on secret sharing for matroid ports.

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Acknowledgements

We thank Dillon Mayhew and Gordon F. Royle for helpful suggestions and also for providing us the matroid database [52]. We thank Guus P. Bollen for his helpful suggestions on algebraic matroids.

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Authors and Affiliations

  1. Universitat Rovira i Virgili, Tarragona, Spain

    Michael Bamiloshin & Oriol Farràs

  2. Ariel University, Ariel, Israel

    Aner Ben-Efraim

  3. Universitat Politècnica de Catalunya, Barcelona, Spain

    Carles Padró

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  1. Michael Bamiloshin
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  2. Aner Ben-Efraim
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  3. Oriol Farràs
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  4. Carles Padró
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Correspondence to Oriol Farràs.

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Communicated by C. Blundo.

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Michael Bamiloshin and Oriol Farràs were supported by the grant 2017 SGR 705 from the Government of Catalonia and Grant RTI2018-095094-B-C21 “CONSENT” from the Spanish Government. Also, Michael Bamiloshin has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 713679 and from the Universitat Rovira i Virgili. Aner Ben-Efraim was supported by ISF Grant 152/17. Carles Padró was supported by the Spanish Government through Grant MTM2016-77213-R.

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Bamiloshin, M., Ben-Efraim, A., Farràs, O. et al. Common information, matroid representation, and secret sharing for matroid ports. Des. Codes Cryptogr. 89, 143–166 (2021). https://doi.org/10.1007/s10623-020-00811-1

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