357 citations
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math.CO2002
The Shadow Theory of Modular and Unimodular Lattices
E. M. Rains, N. J. A. Sloane
It is shown that an n-dimensional unimodular lattice has minimal norm at most 2[n/24] +2, unless n = 23 when the bound must be increased by 1. This result was previously known only…
math.CO2002★ 1 cited
Asymmetric Multiple Description Lattice Vector Quantizers
Suhas N. Diggavi, N. J. A. Sloane, Vinay A. Vaishampayan
We consider the design of asymmetric multiple description lattice quantizers that cover the entire spectrum of the distortion profile, ranging from symmetric or balanced to success…
math.CO2002★ 17 cited
On Cayley's Enumeration of Alkanes (or 4-Valent Trees)
E. M. Rains, N. J. A. Sloane
Cayley's 1875 enumerations of centered and bicentered alkanes (unlabeled trees of valency at most 4) are corrected and extended -- possibly for the first time in 124 years.