Abstract
A set of words with the property that no prefix of any word is the suffix of any other word is called cross-bifix-free set. We provide an efficient generating algorithm producing Gray codes for a remarkable family of cross-bifix-free sets.
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Bajic, D.: On construction of cross-bifix-free kernel sets. 2nd MCM COST 2100, TD(07)237. Lisbon, Portugal (2007)
Bajic, D.: A simple suboptimal construction of cross-bifix-free codes. Crypt. Commun. 6(1), 27–37 (2014)
Baril, J., Vajnovszki, V.: Gray code for derangements. Discret. Appl. Math. 140, 207–221 (2004)
Berstel, J., Perrin, D., Reutenauer, C.: Codes and automata (Encyclopedia of Mathematics and its Applications). Cambridge University Press (2009)
Bilotta, S., Pergola, E., Pinzani, R.: A new approach to cross-bifix-free sets. IEEE Trans. Inf. Theory 58, 4058–4063 (2012)
Chee, Y.M., Kiah, H.M., Purkayastha, P., Wang, C.: Cross-bifix-free codes within a constant factor of optimality. IEEE Trans. Inf. Theory 59, 4668–4674 (2013)
Crochemore, M., Hancart, C., Lecroq, T.: Algorithms on strings. Cambridge University Press, Cambridge (2007)
Er, M.C.: On generating the N-ary reflected Gray code. IEEE Trans. Comput. 33, 739–741 (1984)
Gray, F.: Pulse code communication. U.S. Patent 2(632), 058 (1953)
Hamming, R.W.: Error detecting and error correcting codes. Bell Syst. Tech. J. 29, 147–160 (1950)
Joichi, J., White, D.E., Williamson, S.G.: Combinatorial gray codes. Siam J. Comput. 9, 130–141 (1980)
Knuth, D.E.: The art of computer programming. Vol. 3, sorting and searching. Addison-Wesley, Reading, MA (1973)
Levesque, C.: On m-th order linear recurrences. Fibonacci Quart. 23, 290–293 (1985)
de Lind van Wijngaarden, A.J., Willink, T.J.: Frame synchronization using distributed sequences. IEEE Trans. Commun. 48, 2127–2138 (2000)
Ludman, J.E.: Gray code generation for MPSK signals. IEEE Trans. Commun. 29, 1519–1522 (1981)
Johnson, S.M.: Generation of permutations by adjacent transpositions. Math. Comp. 17, 282–285 (1963)
Nielsen, P.T.: A note on Bifix-free sequences. IEEE Trans. Inf. Theory 29, 704–706 (1973)
Shork, M.: The r-generalized Fibonacci numbers and Polynomial coefficients. Int. J. Contemp. Math. Sci. 3, 1157–1163 (2008)
Vajnovszki, V.: Gray visiting Motzkin. Acta Informatica 38, 793–811 (2002)
Walsh, T.: Gray codes for involutions. J. Comb. Math. Comb. Comput. 36, 95–118 (2001)
Walsh, T.: Generating gray codes in O(1) worst-case time per word. Lect. Notes Comput. Sci 2731, 73–88 (2003)
Williamson, S.G.: Combinatorics for computer science. Computer Science Press, Maryland (1985)
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Bernini, A., Bilotta, S., Pinzani, R. et al. Prefix partitioned gray codes for particular cross-bifix-free sets. Cryptogr. Commun. 6, 359–369 (2014). https://doi.org/10.1007/s12095-014-0105-6
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DOI: https://doi.org/10.1007/s12095-014-0105-6