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189Manuscript: 2442 Abstract Background:SARS-CoV-2 test kits are in critical shortage in many countries. This limits large-scale population testing and hinders the effort to identify and isolate infected individuals. Objectives:Herein, we developed and evaluated multi-stage group testing schemes that test samples in groups of various pool sizes in multiple stages. Through this approach, groups of negative samples can be eliminated with a single test, avoiding the need for individual testing and achieving considerable savings of resources. Study design:We designed and parameterized various multi-stage testing schemes and compared their efficiency at different prevalence rates using computer simulations. Results:We found that three-stage testing schemes with pool sizes of maximum 16 samples can test up to three and seven times as many individuals with the same number of test kits for prevalence rates of around 5% and 1%, respectively. We propose an adaptive approach, where the optimal testing scheme is selected based on the expected prevalence rate. Conclusion:These group testing schemes could lead to a major reduction in the number of testing kits required and help improve large-scale population testing in general and in the context of the current COVID-19 pandemic.

This work provides the first explicit and nonrandom family of [[N, K, D]] LDPC quantum codes which encode K ∈ Θ(N 4 5 ) logical qubits with distance D ∈ Ω(N 3 5 ). The family is constructed by amalgamating classical codes and Ramanujan graphs via an operation called balanced product.Recently, Hastings-Haah-O'Donnell and Panteleev-Kalachev were the first to show that there exist families of LDPC quantum codes which break the polylog(N ) √ N distance barrier. However, their constructions are based on probabilistic arguments which only guarantee the code parameters with high probability whereas our bounds hold unconditionally.Further, balanced products allow for non-abelian twisting of the check matrices, leading to a construction of LDPC quantum codes that can be shown to have K ∈ Θ(N ) and that we conjecture to have linear distance D ∈ Θ(N ).

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We show how the Tutte polynomial of a matroid M can be computed from its condensed configuration, which is a statistic of its lattice of cyclic flats. The results imply that the Tutte polynomial of M is already determined by the abstract lattice of its cyclic flats together with their cardinalities and ranks. They furthermore generalize a similiar statement for perfect matroid designs due to Mphako [4] and help to understand families of matroids with identical Tutte polynomial as constructed in [7].

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