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Abstract For a set Ω = {1, 2, . . . , n} where n = 2k ≥ 6, let Ω{k} denote the set of all subsets of Ω of… Click to show full abstract
Abstract For a set Ω = {1, 2, . . . , n} where n = 2k ≥ 6, let Ω{k} denote the set of all subsets of Ω of size k. We examine the binary codes from the row span of biadjacency matrices of bipartite graphs with bipartition (Ω{k}, Ω{k+1}) and two vertices as k-subsets and (k+1)-subsets of Ω being adjacent if they have one element in common. We show that S2k is contained in the automorphism group of the graphs and the codes, respectively. In addition, we determine the duals of the codes, and by identifying suitable information sets, we construct 2-PD sets for the dual codes.
Keywords:
bipartite graphs;
binary codes;
codes partial;
biadjacency matrices;
matrices bipartite
Journal Title: Quaestiones Mathematicae
Year Published: 2019
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Journal Title: Quaestiones Mathematicae
Year Published: 2019
Link to full text (if available)
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recommendations!