Searching for authors named "Jennifer Seberry" – sorted by Relevance.
88 documents found, showing 1 through 10.
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Bose's Method of Differences Applied to Construct Bhaskar Rao Designs
- …In this paper we show that BIBD(v; b; r; k; ), where v = pq or pq + 1, when written in the notation of Bose's method of differences may often be used to find generalized Bhaskar Rao designs GBRD(p; b 0 ; r 0 ; k; ; G) where G is a group of order q and vice versa. This gives many new GBRDs includ…
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A life’s work on Hadamard matrices, statistical designs, Bent functions and their application to computer and information security and telecommunications
- …One hundred years ago, in 1893, Jacques Hadamard [21] found square matrices of orders 12 and 20, with entries \Sigma1, which had all their rows (and columns) orthogonal. These matrices, X = (x ij), satisfied the equality of the following inequality jdet Xj…
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New Orthogonal Designs and Sequences With Two and Three Variables in Order 28
- …We give new sets of sequences with entries from f0; \Sigmaa; \Sigmab; \Sigmacg on the commuting variables a; b; c and zero autocorrelation function. Then we use these sequences to construct some new orthogonal designs.…
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Generalised Cycling Attacks on RSA
- …Given an RSA modulus n, a ciphertext c and the encryption exponent e, one can construct the sequence x 0 = c mod n; x i+1 = x e i mod n; i = 0; 1; : : : until gcd(x i+1 \Gamma x 0 ; n) 6= 1 or i ? B, B a given boundary. If i B, there are two cases. Case 1: gcd(x i+1 \Gamma x 0 ; n) = n. In this …
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On the Weighing Matrices of Order 4n and Weight 4n-2 and 2n-1
- …We give algorithms and constructions for mathematicaland computer searches which allow us to establish the existence of W (4n; 4n \Gamma 2) and W (4n; 2n \Gamma 1) for many orders 4n less than 4000. We compare these results with the orders for which W (4n; 4n) and W (4n; 2n) are known. We use new al…
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Regular Sets of Matrices and Applications
- …Suppose A 1 ; \Delta \Delta \Delta ; A s are (1; \Gamma1) matrices of order m satisfying A i A j = J; i; j 2 f1; \Delta \Delta \Delta ; sg; (1) A T i A j = A T j A i = J; i 6= j; i; j 2 f1; \Delta \Delta \Delta ; sg; (2) s X i=1 (A i A T i +A T i A i ) = 2smIm ; (3) JA i = A i J = aJ; i = f1…
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On Small Defining Sets for SBIBD(31, 15, 7)
- …The derived design, BIBD(2t \Gamma 1; 4t \Gamma 2; 2t \Gamma 2; t \Gamma 1; t \Gamma 2), of the SBIBD(4t \Gamma 1; 2t \Gamma 1; t \Gamma 1), based on the quadratic residues has been conjectured by Seberry to be uniquely completable to the SBIBD. This paper gives 13 minimal defining sets for this…
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On Circulant Best Matrices and Their Applications
- …Call four type 1 (1; \Gamma1) matrices, X 1 ; X 2 ; X 3 ; X 4 , of the same group of order m (odd) with the properties (i) (X i \GammaI ) T = \Gamma(X i \GammaI ); i = 1; 2; 3 ; (ii) X T 4 = X 4 and the diagonal elements are positive, (iii) X i X j = X j X i and (iv) X 1 X T 1 +X 2 X T 2 +X 3 X T 3 …
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On Infinite Families of Sequences with One and Two Valued Autocorrelation and Two Valued Crosscorrelation Function
- …We show how to construct infinite families of sequences that have one and two valued autocorrelation and two valued crosscorrelation function. These sequences are obtained via the discrete Fourier transform of integer sequences. The sequences obtained can be complex valued or having entries in {0, 1…
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An Algorithm to find Formulae and Values of Minors for Hadamard Matrices
- …We give an algorithm to obtain formulae and values for minors of Hadamard matrices. One step in our algorithm allows the (n j) (n j) minors of an Hadamard matrix to be given in terms of the minors of a 2 j 1 2 j 1 matrix. In particular we illustrate our algorithm by nding explicitly all the (n …
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