Binary codes and partial permutation decoding sets from biadjacency matrices of bipartite graphs Γ(2k, k, k + 1, 1). Issue 4 (2nd April 2020)

• Record Type: Journal Article
• Authors: Fish, W.; Mumba, N.B.; Mwambene, E.; Rodrigues, B.G.
• Is Part Of: Quaestiones mathematicae. Volume 43:Issue 4(2020)
• Page Start: 523
• Page End: 538
• Publication Date: 2020-04-02
• Subjects: 05Axx -- 05Bxx -- 05Cxx -- 15Bxx; Biadjacency matrix -- binary code -- bipartite graphs -- permutation decoding; Mathematics -- Periodicals; 510.5
• DOI: 10.2989/16073606.2019.1580227
• Languages: English
• ISSNs: 1607-3606

Abstract

Abstract: For a set Ω = { 1, 2, . . ., n} where n = 2 k ≥ 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 S 2 k 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.