Tony W. H. Wong

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Quantum synchronizable codes are quantum error-correcting codes that can correct the effects of quantum noise as well as block synchronization errors. We improve the previously known general framework for designing quantum synchronizable codes through more extensive use of the theory of finite fields. This makes it possible to widen the range of tolerable(More)
Let Sn denote the symmetric group on [n] = {1, . . . , n}. A family I ⊆ Sn is intersecting if any two elements of I have at least one common entry. It is known that the only intersecting families of maximal size in Sn are the cosets of point stabilizers. We show that, under mild restrictions, analogous results hold for the alternating group and the direct(More)
We consider integer matrices Nt(h) whose rows are indexed by the t-subsets of an n-set and whose columns are all images of a particular column h under the symmetric group Sn. Earlier work has determined a diagonal form for Nt(h) when h has at least t ‘isolated vertices’ and the results were applied to the binary case of a zero-sum Ramseytype problem of Alon(More)
Relative Bogomolny-Prasad-Sommerfield (BPS) state counts for log Calabi–Yau surface pairs were introduced by Gross–Pandharipande–Siebert in [4] and conjectured by the authors to be integers. For toric del Pezzo surfaces, we provide an arithmetic proof of this conjecture, by relating these invariants to the local BPS state counts of the surfaces. The latter(More)
Let G be a subgraph of a complete bipartite graph Kn,n. Let N(G) be a 0-1 incidence matrix with edges of Kn,n against images of G under the automorphism group of Kn,n. A diagonal form of N(G) is found for every G, and whether the row space of N(G) over Zp contains the vector of all 1’s is determined. This re-proves Caro and Yuster’s results on zero-sum(More)
We consider integer matrices Nt whose rows are indexed by the t-subsets of an n-set and whose columns are all distinct images of a particular column under the symmetric group Sn. Examples include matrices in the association algebras of the Johnson schemes. Three related problems are addressed. What is the Smith normal form (or a diagonal form) for Nt and(More)
This thesis focuses mainly on linear algebraic aspects of combinatorics. Let Nt(H) be an incidence matrix with edges versus all subhypergraphs of a complete hypergraph that are isomorphic to H. Richard M. Wilson and the author find the general formula for the Smith normal form or diagonal form of Nt(H) for all simple graphs H and for a very general class of(More)
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