Geodesic
Nonexistence results for Hadamard-like matrices
The electronic journal of combinatorics, Tome 11 (2004) no. 1
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The class of square $(0,1,-1)$-matrices whose rows are nonzero and mutually orthogonal is studied. This class generalizes the classes of Hadamard and Weighing matrices. We prove that if there exists an $n$ by $n$ $(0,1,-1)$-matrix whose rows are nonzero, mutually orthogonal and whose first row has no zeros, then $n$ is not of the form $p^k$, $2p^k$ or $3p$ where $p$ is an odd prime, and $k$ is a positive integer.
DOI : 10.37236/1842
Classification : 05B20, 15B36 
@article{10_37236_1842,
     author = {Justin D. Christian and Bryan L. Shader},
     title = {Nonexistence results for {Hadamard-like} matrices},
     journal = {The electronic journal of combinatorics},
     year = {2004},
     volume = {11},
     number = {1},
     doi = {10.37236/1842},
     zbl = {1031.05028},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1842/}
}
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Justin D. Christian; Bryan L. Shader. Nonexistence results for Hadamard-like matrices. The electronic journal of combinatorics, Tome 11 (2004) no. 1. doi: 10.37236/1842

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