For k ≥ 1, the odd graph denoted by O(k), is the graph with the vertex-set Ωk, the set of all k-subsets of Ω = 1, 2, …, 2k +1, and any two of its vertices u and v constitute an edge [u, v] if and only if u ∩ v = /0. In this paper the binary code generated by the adjacency matrix of O(k) is studied. The automorphism group of the code is determined, and by identifying a suitable information set, a 2-PD-set of the order of k 4 is determined. Lastly, the relationship between the dual code from O(k) and the code from its graph-theoretical complement , is investigated.
@article{bwmeta1.element.doi-10_2478_s11533-014-0417-y,
author = {Washiela Fish and Roland Fray and Eric Mwambene},
title = {Binary codes and partial permutation decoding sets from the odd graphs},
journal = {Open Mathematics},
volume = {12},
year = {2014},
pages = {1362-1371},
zbl = {06308919},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-014-0417-y}
}
Washiela Fish; Roland Fray; Eric Mwambene. Binary codes and partial permutation decoding sets from the odd graphs. Open Mathematics, Tome 12 (2014) pp. 1362-1371. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-014-0417-y/
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