A note on optimal unimodular lattices

DOI10.1006/jnth.1998.2257zbMath0917.11027arXivmath/0207292OpenAlexW2000054582WikidataQ105443765 ScholiaQ105443765MaRDI QIDQ1273720

N. J. A. Sloane, Conway, John H.

Publication date: 20 July 1999

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0207292

zbMATH Keywords

shadow theta series optimal unimodular lattices

Mathematics Subject Classification ID

Sums of squares and representations by other particular quadratic forms (11E25) Quadratic forms (reduction theory, extreme forms, etc.) (11H55)

Related Items

Minimum message length analysis of multiple short time series, Bounding basis reduction properties, A mass formula for unimodular lattices with no roots, CONSTRUCTION OF SOME UNIMODULAR LATTICES WITH LONG SHADOWS, Properties of real and complex ETFs and their application to the design of low coherence frames, Pauli graphs, Riemann hypothesis, and Goldbach pairs, Laminating lattices with symmetrical glue, Local conformal nets arising from framed vertex operator algebras, Extremal ternary self-dual codes constructed from negacirculant matrices, Wythoffian skeletal polyhedra in ordinary space. I, On the integrality of \(n\)th roots of generating functions, Hyperuniform states of matter, Equations of State for Hard Spheres and Hard Disks, Lattices from codes over \(\mathbb {Z}_q\): generalization of constructions \(D\), \(D'\) and \(\overline{D}\), The complex Lorentzian Leech lattice and the bimonster, Reflection group of the quaternionic Lorentzian Leech lattice, Symmetric box-splines on the \(\mathcal A^*_n\) lattice, Constructions of rotated lattice constellations in dimensions power of 3, Refinability of splines derived from regular tessellations, Connections between Construction D and related constructions of lattices, Computational complexity of reconstruction and isomorphism testing for designs and line graphs, The 3-ball is a local pessimum for packing, 2- and 3-modular lattice wiretap codes in small dimensions, On soccer balls and linearized inverse statistical mechanics, A Practical Fuzzy Extractor for Continuous Features, Modular lattices from a variation of construction A over number fields, Density of triangulated ternary disc packings, Optimal arrangements of classical and quantum states with limited purity, Quaternionic representation of snub 24-cell and its dual polytope derived from \(E_8\) root system., Optimal self-dual \(\mathbb Z_4\)-codes and a unimodular lattice in dimension 41, A Poincaré series on hyperbolic space, Lower bound for the number of nodes of cubature formulae on the unit ball, Perfect codes in the \(\ell_p\) metric, Maximal theta functions universal optimality of the hexagonal lattice for Madelung-like lattice energies, Splitting the shadow., A Gilbert-Varshamov-type bound for lattice packings, On projections of arbitrary lattices, New horizons in sphere-packing theory, part II: Lattice-based derivative-free optimization via global surrogates, Atlas of quasicrystalline tilings., On Siegel modular forms of weigth 12, A note on projecting the cubic lattice, Bounds on three- and higher-distance sets, Protein structure prediction problem: formalization using quaternions, Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions., An optimal odd unimodular lattice in dimension 72, A shadow identity and an application to isoduality., Spherical designs and lattices, \(s\)-extremal strongly modular lattices, Lattice Codes for the Gaussian Wiretap Channel, Algorithms for the Shortest and Closest Lattice Vector Problems, On the most compact regular lattices in large dimensions: A statistical mechanical approach, On the existence of extremal Type II ℤ_{2𝕜}-codes, Generalization of one-dimensional material models for the finite element method, C₇₀, C₈₀, C₉₀and carbon nanotubes by breaking of the icosahedral symmetry of C₆₀, Globally optimized packings of non-uniform size spheres in \(\mathbb {R}^{d}\): a computational study, Multiplicative invariant lattices in \(\mathbb{R}^n\) obtained by twisting of group algebras and some explicit characterizations., Fast Fourier transform on FCC and BCC lattices with outputs on FCC and BCC lattices respectively, Minkowski bisectors, Minkowski cells and lattice coverings, Models in boundary quantum field theory associated with lattices and loop group models, An edge detection approach based on directional wavelet transform, Symmetric box-splines on root lattices, Surgeries of pairing of edges associated to trivalent graphs, On the covering radius problem for ternary self-dual codes, Estimates of the maximal value of angular code distance for 24 and 25 points on the unit sphere in \(\mathbb{R}^4\), On the classification of automorphic products and generalized Kac-Moody algebras, Symplectic Lattice Reduction and NTRU, On some self-dual codes and unimodular lattices in dimension 48, Extremal unimodular lattices in dimension 36, Adaptive coset partition for distributed video coding, On the size of incoherent systems, Automorphic forms, fake monster algebras, and hyperbolic reflection groups, Quasi-perfect codes in the \(\ell _p\) metric, Kneser-Hecke-operators in coding theory, Lattice-based high-dimensional Gaussian filtering and the permutohedral lattice, Niemeier lattices in the free fermionic heterotic-string formulation, A note on the distribution of the distance from a lattice, On lattices whose minimal vectors form a 6-design, An optimal unimodular lattice in dimension 39, Fast and stable evaluation of box-splines via the BB-form, Minimum message length shrinkage estimation, Symmetric representation of the elements of the Conway group \(.0\)., On the existence of frames of the Niemeier lattices and self-dual codes over \(\mathbb F_p\), A note on optimal unimodular lattices, Rationality and \(p\)-adic properties of reduced forms of half-integral weight, Construction of new extremal unimodular lattices, On Coxeter diagrams of complex reflection groups, Spherical codes, maximal local packing density, and the golden ratio, Classification of positive definite lattices, Self-dual codes over \(\mathbb{F}_5\) and \(s\)-extremal unimodular lattices, On odd rank integral quadratic forms: canonical representatives of projective classes and explicit construction of integral classes with square-free determinant, Algebraic constructions of densest lattices, Zagier duality and integrality of Fourier coefficients for weakly holomorphic modular forms, A Gleason formula for Ozeki polynomials, Ternary code construction of unimodular lattices and self-dual codes over \(\mathbb Z_6\), When is the ball a local pessimum for covering?

Cites Work