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

• Published in: Discrete Applied Mathematics Vol. 179; pp. 193 - 200
• Main Authors: Östergård, Patric R.J., Pettersson, Ville H.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 31-12-2014
• Subjects: Augmentation; Canonical augmentation; Circuit code; Circuits; Coil-in-the-box code; Coiling; Induced cycle; Mathematical analysis; Snake-in-the-box code; Spreads; Coil-in-the-box code; Canonical augmentation; Induced cycle; Snake-in-the-box code; Circuit code
• ISSN: 0166-218X; 1872-6771
• DOI: 10.1016/j.dam.2014.07.010

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.