Cryptography and Communications

, Volume 10, Issue 4, pp 667–683 | Cite as

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

  • Elena Barcucci
  • Antonio BerniniEmail author
  • Stefano Bilotta
  • Renzo Pinzani


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.


Bidimensional codes Non-overlapping matrices Restricted words 

Mathematics Subjects Classification (2010)

68R15 94B25 05A15 



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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© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Dipartimento di Matematica e Informatica “U. Dini”Universitá degli Studi di FirenzeFirenzeItaly

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