Abstract
A code which does not require a distinct symbol to separate code words is called comma-free. We study comma-free codes with words of length 2 by considering the binary relation the code defines on its alphabet. If the code is a maximal comma-free code we show that the relation it defines is the support relation of an incidence algebra and its complementary relation will also define an incidence algebra.
Keywords
- Code Word
- Triangular Matrice
- Support Relation
- Complementary Relation
- Distinct Symbol
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References
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D.A. Smith, Incidence functions as generalized arithmetic functions I, Duke Math. J. 34 (1967), 617–633.
D.A. Smith, Incidence functions as generalized arithmetic functions II, Duke Math. J. 36 (1969), 15–30.
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© 1976 Springer-Verlag
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Cummings, L.J. (1976). Comma-free codes and incidence algebras. In: Casse, L.R.A., Wallis, W.D. (eds) Combinatorial Mathematics IV. Lecture Notes in Mathematics, vol 560. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097363
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DOI: https://doi.org/10.1007/BFb0097363
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-08053-4
Online ISBN: 978-3-540-37537-1
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