A feasibility approach for constructing combinatorial designs of circulant type
Combinatorics
2018-08-13 v1 Optimization and Control
Abstract
In this work, we propose an optimization approach for constructing various classes of circulant combinatorial designs that can be defined in terms of autocorrelations. The problem is formulated as a so-called feasibility problem having three sets, to which the Douglas-Rachford projection algorithm is applied. The approach is illustrated on three different classes of circulant combinatorial designs: circulant weighing matrices, D-optimal matrices, and Hadamard matrices with two circulant cores. Furthermore, we explicitly construct two new circulant weighing matrices, a and a , whose existence was previously marked as unresolved in the most recent version of Strassler's table.
Cite
@article{arxiv.1711.02502,
title = {A feasibility approach for constructing combinatorial designs of circulant type},
author = {Francisco J. Aragón Artacho and Rubén Campoy and Ilias Kotsireas and Matthew K. Tam},
journal= {arXiv preprint arXiv:1711.02502},
year = {2018}
}