On the maximum length of coil-in-the-box codes in dimension 8

On the maximum length of coil-in-the-box codes in dimension 8

The coil-in-the-box problem asks for a simple chordless cycle of maximum length in the n-cube. Such cycles are also known as n-dimensional spread 2 circuit codes, or n-coils. This problem has been solved earlier for n≤7. An approach based on canonical augmentation is here used to solve the problem f...

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Veröffentlicht in:Discrete Applied Mathematics 2014-12, Vol.179, p.193-200
Hauptverfasser: Östergård, Patric R.J., Pettersson, Ville H.
Format: Artikel
Sprache:eng
Schlagworte:
Augmentation
Canonical augmentation
Circuit code
Circuits
Coil-in-the-box code
Coiling
Induced cycle
Mathematical analysis
Snake-in-the-box code
Spreads
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Zusammenfassung:The coil-in-the-box problem asks for a simple chordless cycle of maximum length in the n-cube. Such cycles are also known as n-dimensional spread 2 circuit codes, or n-coils. This problem has been solved earlier for n≤7. An approach based on canonical augmentation is here used to solve the problem for n=8 and show that the maximum length of a chordless cycle in the 8-cube is 96. Several new 8-coils of length 96 are presented.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2014.07.010