G. H. John van Rees

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A critical set in a latin square is a set of entries in a latin square which can be embedded in only one latin square. Also, if any element of the critical set is deleted, the remaining set can be embedded in more than one latin square. A critical set is strong if the embedding latin square is particularly easy to find because the remaining squares of the(More)
The shares in a (k, n) Shamir threshold scheme consist of n points on some polynomial of degree at most k − 1. If one or more of the shares are faulty, then the secret may not be reconstructed correctly. Supposing that at most t of the n shares are faulty, we show how a suitably chosen covering design can be used to compute the correct secret. We review(More)
A binary self-dual code of length 2k is a (2k, k) binary linear code C with the property that every pair of codewords in C are orthogonal. Two self-dual codes, C1 and C2, are equivalent if and only if there is a permutation of the coordinates of C1 that takes C1 into C2. The automorphism group of a binary code C is the set of all permutations of the(More)
J. S. Berg, A. Blondel, A. Bogacz, S. Brooks, J.-E. Campagne, D. Caspar, C. Cevata, P. Chimenti, J. Cobb, M. Dracos, R. Edgecock, I. Efthymiopoulos, A. Fabich, R. Fernow, F. Filthaut, J. Gallardo, R. Garoby, S. Geer, F. Gerigk, G. Hanson, R. Johnson, C. Johnstone, D. Kaplan, E. Keil, H. Kirk, A. Klier, A. Kurup, J. Lettry, K. Long, S. Machida, K. McDonald,(More)
A critical set in a latin square is a subset of its elements with the following properties: 1) No other latin square exists which also contains that subset. 2) No element may be deleted without destroying property 1. Let scs(n) denote the smallest possible cardinality of a critical set in an n × n latin square. It is conjectured that scs(n) = n/4 , and that(More)
Suppose m and t are integers such that 0 < t ≤ m. An (m, t) splitting system is a pair (X,B) where |X| = m, B is a set of bm2 c subsets of X, called blocks such that for every Y ⊆ X and |Y | = t, there exists a block B ∈ B such that |B ∩Y | = b t 2c or |(X \B)∩Y | = b t 2c. We will give some results on splitting systems for t = 2 or 4 which often depend on(More)