A feasibility approach for constructing combinatorial designs of circulant type
arXiv:1711.02502 · doi:10.1007/s10878-018-0250-5
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.
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