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View all- Holmes MSalisbury T(2014)Degenerate random environmentsRandom Structures & Algorithms10.1002/rsa.2047345:1(111-137)Online publication date: 1-Aug-2014
Let A(n,d) denote the maximum possible number of codewords in a binary code of length n and minimum Hamming distance d. For large values of n, the best known upper bound, for fixed d, is the Johnson bound. We give a new upper bound which is at least as ...
The hexagonal lattice site percolation critical probability is shown to be at most 0.79472, improving the best previous mathematically rigorous upper bound. The bound is derived by using the substitution method to compare the site model with the bond ...
Rigorous bounds for the bond percolation critical probability are determined for three Archimedean lattices: .7385 < pc((3, 122) bond) < .7449, .6430 < pc((4, 6, 12) bond) < .7376, .6281 < pc((4, 82) bond) < .7201. Consequently, the bond percolation ...
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