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- W2964138304 abstract "We present some observations on a restricted variant of unitary Cayley graphs modulo $n$, and implications for a decomposition of elements of symplectic operators over the integers modulo $n$. We define quadratic unitary Cayley graphs $G_n$, whose vertex set is the ring ${Bbb Z}_n$, and where residues $a,b$ modulo $n$ are adjacent if and only if their difference is a quadratic residue. By bounding the diameter of such graphs, we show an upper bound on the number of elementary operations (symplectic scalar multiplications, symplectic row swaps, and row additions or subtractions) required to decompose a symplectic matrix over ${Bbb Z}_n$. We also characterize the conditions on $n$ for $G_n$ to be a perfect graph." @default.
- W2964138304 created "2019-07-30" @default.
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- W2964138304 date "2010-05-07" @default.
- W2964138304 modified "2023-09-30" @default.
- W2964138304 title "On Restricted Unitary Cayley Graphs and Symplectic Transformations Modulo $n$" @default.
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- W2964138304 doi "https://doi.org/10.37236/341" @default.
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