Washiela Fish

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We show how to find s-PD-sets of size s + 1 that satisfy the Gordon-Schönheim bound for partial permutation decoding for the binary simplex codes S n (F 2) for all n ≥ 4, and for all values of s up to 2 n −1 n − 1. The construction also applies to the q-ary simplex codes S n (F q) for q > 2, and to s-antiblocking information systems of size s + 1, for s up(More)
For integers n ≥ 1, k ≥ 0, and k ≤ n, the graph Γ k n has vertices the 2 n vectors of F n 2 and adjacency defined by two vectors being adjacent if they differ in k coordinate positions. In particular Γ 1 n is the n-cube, usually denoted by Q n. We examine the binary codes obtained from the adjacency matrices of these graphs when k = 1, 2, 3, following(More)
We examine the binary codes C2(Ai + I) from matrices Ai + I where Ai is an adjacency matrix of a uniform subset graph Γ(n, 3, i) of 3-subsets of a set of size n with adjacency defined by subsets meeting in i elements of Ω, where 0 ≤ i ≤ 2. Most of the main parameters are obtained; the hulls, the duals, and other subcodes of the C2(Ai + I) are also examined.(More)
The Johnson graph, denoted by J(n, k), is the graph of which the vertex-set is the set of all k-subsets of Ω = {1, 2,. .. , n}, and any two vertices u and v constitute an edge [u, v] if and only if |u ∩ v| = k − 1. In this talk the codes and their duals generated by the adjacency matrix of J(n, k) will be described. It will be shown that in each case, the(More)
  • W. Fish
  • 2016
Let $$n, m \ge 2$$ n , m ≥ 2 be integers. The cartesian, categorical and lexicographic products of m copies of the n-cycle denoted by $$C_n$$ C n all have as their vertex-set $$\{0, 1, \ldots , n-1\}^m$$ { 0 , 1 , … , n - 1 } m , with adjacency defined variously. In this paper the binary codes generated by the row span of adjacency matrices of the(More)