Binary codes and partial permutation decoding sets from biadjacency matrices of bipartite graphs Γ(2k, k, k + 1, 1)

2019 ◽  
Vol 43 (4) ◽  
pp. 523-538 ◽  
Author(s):  
W. Fish ◽  
N.B. Mumba ◽  
E. Mwambene ◽  
B.G. Rodrigues
Keyword(s):  
Bipartite Graphs ◽  
Binary Codes ◽  
Permutation Decoding

Codes from multipartite graphs and minimal permutation decoding sets

2015 ◽  
Vol 07 (04) ◽  
pp. 1550060
Author(s):  
P. Seneviratne
Keyword(s):  
Automorphism Group ◽  
Error Correcting Code ◽  
Binary Codes ◽  
Hard Problem ◽  
Complete Multipartite Graph ◽  
Decoding Algorithm ◽  
Permutation Decoding ◽  
Multipartite Graphs ◽  
Multipartite Graph ◽  
Complete Multipartite

Permutation decoding method developed by MacWilliams and described in [Permutation decoding of systematic codes, Bell Syst. Tech. J. 43 (1964) 485–505] is a decoding technique that uses a subset of the automorphism group of the code called a PD-set. The complexity of the permutation decoding algorithm depends on the size of the PD-set and finding a minimal PD-set for an error correcting code is a hard problem. In this paper we examine binary codes from the complete-multipartite graph [Formula: see text] and find PD-sets for all values of [Formula: see text] and [Formula: see text]. Further we show that these PD-sets are minimal when [Formula: see text] is odd and [Formula: see text].

scholarly journals Permutation decoding for binary codes from lattice graphs

2008 ◽  
Vol 308 (13) ◽  
pp. 2862-2867 ◽  
Author(s):  
J.D. Key ◽  
P. Seneviratne
Keyword(s):  
Binary Codes ◽  
Permutation Decoding ◽  
Lattice Graphs

Binary codes and partial permutation decoding sets from the odd graphs

2014 ◽  
Vol 12 (9) ◽  
Author(s):  
Washiela Fish ◽  
Roland Fray ◽  
Eric Mwambene
Keyword(s):  
Automorphism Group ◽  
Adjacency Matrix ◽  
Binary Code ◽  
Dual Code ◽  
Binary Codes ◽  
Permutation Decoding ◽  
Vertex Set ◽  
Information Set ◽  
The Relationship

AbstractFor 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 ∩ 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 $\overline {O(k)} $, is investigated.

scholarly journals Permutation decoding for the binary codes from triangular graphs

2004 ◽  
Vol 25 (1) ◽  
pp. 113-123 ◽  
Author(s):  
J.D. Key ◽  
J. Moori ◽  
B.G. Rodrigues
Keyword(s):  
Binary Codes ◽  
Permutation Decoding
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