Canonical Form of Gray Codes in N-cubes

Abstract : In previous works, the idea of walking into a $\mathsf {N}$-cube where a balanced Hamiltonian cycle have been removed has been proposed as the basis of a chaotic PRNG whose chaotic behavior has been proven. However, the construction and selection of the most suited balanced Hamiltonian cycles implies practical and theoretical issues. We propose in this paper a canonical form for representing isomorphic Gray codes. It provides a drastic complexity reduction of the exploration of all the Hamiltonian cycles and we discuss some criteria for the selection of the most suited cycles for use in our chaotic PRNG.
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Submitted on : Tuesday, December 5, 2017 - 3:41:59 PM
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Sylvain Contassot-Vivier, Jean-François Couchot. Canonical Form of Gray Codes in N-cubes. 23th International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA), Jun 2017, Milan, Italy. pp.68-80, ⟨10.1007/978-3-319-58631-1_6 ⟩. ⟨hal-01656349⟩

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