5 research outputs found
Isodual and Self-dual Codes from Graphs
Binary linear codes are constructed from graphs, in particular, by the
generator matrix where is the adjacency matrix of a graph on
vertices. A combinatorial interpretation of the minimum distance of such codes
is given. We also present graph theoretic conditions for such linear codes to
be Type I and Type II self-dual. Several examples of binary linear codes
produced by well-known graph classes are given
Binary codes from m-ary n-cubes Q(n) (m)
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 its dual, and show the codes to be LCD. We also
nd s-PD-sets of size s + 1 for s < m1
2 for the dual codes, i.e. [m2; 2m 1;m]2 codes, when
n = 2 and m 5 is odd
Codes from adjacency matrices of uniform subset graphs
Studies of the p-ary codes from the adjacency matrices of uniform subset graphs Γ(n,k,r)Γ(n,k,r) and their reflexive associates have shown that a particular family of codes defined on the subsets are intimately related to the codes from these graphs. We describe these codes here and examine their relation to some particular classes of uniform subset graphs. In particular we include a complete analysis of the p-ary codes from Γ(n,3,r)Γ(n,3,r) for p≥5p≥5 , thus extending earlier results for p=2,3p=2,3