Computation of maximal determinants of binary circulant matrices
RP Brent, AB Yedidia - arXiv preprint arXiv:1801.00399, 2018 - arxiv.org
arXiv preprint arXiv:1801.00399, 2018•arxiv.org
We describe algorithms for computing maximal determinants of binary circulant matrices of
small orders. Here" binary matrix" means a matrix whose elements are drawn from $\{0, 1\} $
or $\{-1, 1\} $. We describe efficient parallel algorithms for the search, using Duval's
algorithm for generation of necklaces and the well-known representation of the determinant
of a circulant in terms of roots of unity. Tables of maximal determinants are given for orders
$\le 53$. Our computations extend earlier results and disprove two plausible conjectures.
small orders. Here" binary matrix" means a matrix whose elements are drawn from $\{0, 1\} $
or $\{-1, 1\} $. We describe efficient parallel algorithms for the search, using Duval's
algorithm for generation of necklaces and the well-known representation of the determinant
of a circulant in terms of roots of unity. Tables of maximal determinants are given for orders
$\le 53$. Our computations extend earlier results and disprove two plausible conjectures.
We describe algorithms for computing maximal determinants of binary circulant matrices of small orders. Here "binary matrix" means a matrix whose elements are drawn from or . We describe efficient parallel algorithms for the search, using Duval's algorithm for generation of necklaces and the well-known representation of the determinant of a circulant in terms of roots of unity. Tables of maximal determinants are given for orders . Our computations extend earlier results and disprove two plausible conjectures.
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