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A 2D non-overlapping code over a q-ary alphabet

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Abstract

We define a set of matrices over a finite alphabet where all possible overlaps between any two matrices are forbidden. The set is also enumerated by providing some recurrences counting particular classes of restricted words. Moreover, we analyze the asymptotic cardinality of the set according to the parameters related to the construction of the matrices.

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Acknowledgements

This work has been partially supported by the PRIN project “Automi e linguaggi formali: aspetti matematici ed applicativi”, GNCS project “Strutture discrete con vincoli” and GNCS project “Codici di stringhe e matrici non sovrapponibili”. The authors would like to thank the anonymous referee for his valuable advices about the asymptotics.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica “U. Dini”, Universitá degli Studi di Firenze, Viale G.B. Morgagni 65, 50134, Firenze, Italy

    Elena Barcucci, Antonio Bernini, Stefano Bilotta & Renzo Pinzani

Authors
  1. Elena Barcucci
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  2. Antonio Bernini
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  3. Stefano Bilotta
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  4. Renzo Pinzani
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Correspondence to Antonio Bernini.

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Barcucci, E., Bernini, A., Bilotta, S. et al. A 2D non-overlapping code over a q-ary alphabet. Cryptogr. Commun. 10, 667–683 (2018). https://doi.org/10.1007/s12095-017-0251-8

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  • DOI: https://doi.org/10.1007/s12095-017-0251-8

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