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Abstract
A cubelike graph is a Cayley graph for the elementary abelian group of order 2^{n}. In studies of the chromatic number of cubelike graphs, the kth power of the ndimensional hypercube, Q_{n} ^{k}, is frequently considered. This coloring problem can be considered in the framework of coding theory, as the graph Q_{n} ^{k} can be constructed with one vertex for each binary word of length n and edges between vertices exactly when the Hamming distance between the corresponding words is at most k. Consequently, a proper coloring of Q_{n} ^{k} corresponds to a partition of the ndimensional binary Hamming space into codes with minimum distance at least k + 1. The smallest open case, the chromatic number of Q_{8} ^{2}, is here settled by finding a 13coloring. Such 13colorings with specific symmetries are further classified.
Original language  English 

Pages (fromto)  25512561 
Number of pages  11 
Journal  Mathematics of Computation 
Volume  87 
Issue number  313 
DOIs  
Publication status  Published  1 Jan 2018 
MoE publication type  A1 Journal articlerefereed 
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Dive into the research topics of 'The chromatic number of the square of the 8cube'. Together they form a unique fingerprint.Projects
 1 Finished

Construction and Classification of Discrete Mathematic Structures
Kokkala, J., Laaksonen, A., Östergård, P., Szollosi, F. & Pöllänen, A.
01/09/2015 → 31/08/2019
Project: Academy of Finland: Other research funding