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- Washiela Fish, Jennifer D. Key, Eric C. Mwambene
- Discrete Mathematics
- 2011

- Jennifer D. Key, Washiela Fish, Eric C. Mwambene
- Adv. in Math. of Comm.
- 2011

- Washiela Fish, Jennifer D. Key, Eric C. Mwambene
- Discrete Mathematics
- 2010

- Washiela Fish, Jennifer D. Key, Eric C. Mwambene
- J. Symb. Comput.
- 2010

We examine designs and binary codes associated with the line graph of the n-cube Qn, i.e. the Hamming graph H(n, 2). We find the automorphism groups and the parameters of the codes. We find a regular subgroup of the automorphism group that can be used for permutation decoding, or partial permutation decoding, for any information set.

- Washiela Fish, Jennifer D. Key, Eric C. Mwambene
- Adv. in Math. of Comm.
- 2012

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)

- Washiela Fish, Jennifer D. Key, Eric C. Mwambene
- Discrete Mathematics
- 2009

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)

- Washiela Fish, Jennifer D. Key, Eric C. Mwambene
- Adv. in Math. of Comm.
- 2015

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)

- W. Fish
- Applicable Algebra in Engineering, Communication…
- 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)

- Washiela Fish, Khumbo Kumwenda, Eric C. Mwambene
- Ars Comb.
- 2012

- Washiela Fish
- Graphs and Combinatorics
- 2015

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)