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Binary codes and partial permutation decoding sets from the odd graphs
(Walter de Gruyter, 2014)
For k ≥ 1, the odd graph denoted by O(k), is the graph with the vertex-set Ω{k}
, 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 ∩ ...
Graphs, designs and codes related to the n-cube
(Elsivier, 2009)
For integers n 1; k 0, and k n, the graph k
n has vertices the 2n vectors of
Fn
2 and adjacency defined by two vectors being adjacent if they differ in k coordinate
positions. In particular 1
n is the ...
Binary codes from m-ary n-cubes Q(n) (m)
(American Institute of Mathematical Sciences, 2021)
We examine the binary codes from adjacency matrices of the graph with vertices the nodes
of the m-ary n-cube Qmn
and with adjacency de ned by the Lee metric. For n = 2 and m odd,
we obtain the parameters of the code and ...