Computation of Maximal Determinants of Binary Circulant Matrices
Combinatorics
2021-02-23 v6 Discrete Mathematics
Abstract
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.
Cite
@article{arxiv.1801.00399,
title = {Computation of Maximal Determinants of Binary Circulant Matrices},
author = {Richard P. Brent and Adam B. Yedidia},
journal= {arXiv preprint arXiv:1801.00399},
year = {2021}
}
Comments
22 pages, 4 tables. Improved analysis of quantile estimation in v4, Table 2 updated in v5, Table 4 updated in v6