Sets of disjoint snakes based on a Reed-Muller code and covering the hypercube |
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Authors: | A J van Zanten Loeky Haryanto |
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Institution: | (1) Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, P.O. Box 5031, Delft, 2600 GA, The Netherlands;(2) Department of Mathematics, Hasanuddin University, Kampus Tamalanrea, Makassar, 90245, Indonesia |
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Abstract: | A snake-in-the-box code (or snake) of word length n is a simple circuit in an n-dimensional cube Q
n
, with the additional property that any two non-neighboring words in the circuit differ in at least two positions. To construct
such snakes a straightforward, non-recursive method is developed based on special linear codes with minimum distance 4. An
extension of this method is used for the construction of covers of Q
n
consisting of 2
m-1 vertex-disjoint snakes, for 2
m-1 < n ≤ 2
m
. These covers turn out to have a symmetry group of order 2
m
.
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Keywords: | Snake-in-the-box-code Snake Gray code Reed-Muller code Parallel system Cover Invariance group |
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