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Combinatorial Designs and Applications, 2020
J. Seberry, Mieko Yamada
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J. Seberry, Mieko Yamada
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On Pless symmetry codes, ternary QR codes, and related Hadamard matrices and designs
Designs, Codes and Cryptography, 2021It is proved that a code L ( q ) which is monomially equivalent to the Pless symmetry code C ( q ) of length $$2q+2$$ 2 q + 2 contains the (0,1)-incidence matrix of a Hadamard 3- $$(2q+2,q+1,(q-1)/2)$$ ( 2 q + 2 , q + 1 , ( q - 1 ) / 2 ) design D ( q ...
V. Tonchev
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Classification of skew‐Hadamard matrices of order 32 and association schemes of order 31
Journal of combinatorial designs (Print), 2020Using a backtracking algorithm along with an essential change to the rows of representatives of known 13 710 027 equivalence classes of Hadamard matrices of order 32, we make an exhaustive computer search feasible and show that there are exactly 6662 ...
A. Hanaki +3 more
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Designs, Codes and Cryptography, 1997
Let \(\pi\) be a projective plane of order \(n\) such that \(\pi\) admits a group \(G\) of \(n\) elations each with axis \(L\) and center \(P\in L\). The existence of the elation group \(G\) is equivalent to the existence of a matrix \(H=(g_{ij})\) of order \(n\) with entries \(g_{ij}\) from \(G\) such that whenever \(m\not= k\) the set \(\{g_{mi}g_{ki}
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Let \(\pi\) be a projective plane of order \(n\) such that \(\pi\) admits a group \(G\) of \(n\) elations each with axis \(L\) and center \(P\in L\). The existence of the elation group \(G\) is equivalent to the existence of a matrix \(H=(g_{ij})\) of order \(n\) with entries \(g_{ij}\) from \(G\) such that whenever \(m\not= k\) the set \(\{g_{mi}g_{ki}
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Graphs and Combinatorics, 1987
This paper gives constructive methods for embedding a dicyclic solution of a balanced incomplete block design with parameters \((2t+1,4t+2,2t,t,t- 1)\) in a Hadamard matrix of order \(4t+4\). In a recent paper [Three new dicyclic solutions of (21,42,20,10,9)-designs, J. Comb. Theory, Ser.
Bhat-Nayak, V. N. +2 more
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This paper gives constructive methods for embedding a dicyclic solution of a balanced incomplete block design with parameters \((2t+1,4t+2,2t,t,t- 1)\) in a Hadamard matrix of order \(4t+4\). In a recent paper [Three new dicyclic solutions of (21,42,20,10,9)-designs, J. Comb. Theory, Ser.
Bhat-Nayak, V. N. +2 more
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1972
Dataset shows discoveries made by the author relating to Hadamard matrices.
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Dataset shows discoveries made by the author relating to Hadamard matrices.
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Higher-dimensional Hadamard matrices
IEEE Transactions on Information Theory, 1979The concept of a Hadamard matrix as a binary orthogonal matrix is extended to higher dimensions. An n -dimensional Hadamard matrix [h_{ijk \cdots n}] is defined as one in which all parallel (n - 1) -dimensional layers, in any axis-normal orientation, are uncorrelated. This is equivalent to the requirements that h_{ijk \cdots n} = \pm1 and that \sum_{p}
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Self-dual bent sequences for complex Hadamard matrices
Designs, Codes and Cryptography, 2022Minjia Shi +5 more
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Classifying Cocyclic Butson Hadamard Matrices
, 2015We classify all the cocyclic Butson Hadamard matrices BH(n, p) of order n over the pth roots of unity for an odd prime p and n p ≤ 100. That is, we compile a list of matrices such that any cocyclic BH(n, p) for these n, p is equivalent to exactly one ...
Ronan Egan +2 more
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