Lattices and Codes

DOI10.1007/978-3-658-00360-9zbMath1257.11066OpenAlexW4233469339MaRDI QIDQ2917597

Publication date: 1 October 2012

Published in: Advanced Lectures in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-658-00360-9

Mathematics Subject Classification ID

Linear codes (general theory) (94B05) Lattices and convex bodies (number-theoretic aspects) (11H06) Theta series; Weil representation; theta correspondences (11F27) Quadratic forms over global rings and fields (11E12) Holomorphic modular forms of integral weight (11F11) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory (11-01) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to information and communication theory (94-01) Quadratic forms (reduction theory, extreme forms, etc.) (11H55) Relations with coding theory (11H71)

Related Items

Connected components of the moduli of elliptic $K3$ surfaces ⋮ Rational double points on Enriques surfaces ⋮ A note on Assmus-Mattson type theorems ⋮ Self-dual codes over ${\mathbb{F}}_2[u/\langle u^4 \rangle$ and Jacobi forms over a totally real subfield of ${\mathbb{Q}}(\zeta_8)$] ⋮ Divisible $\mathbb{Z}$-modules ⋮ Lattice of $\mathbb{Z}$-module ⋮ The isospectral problem for flat tori from three perspectives ⋮ Lattice Encoding of Cyclic Codes from Skew-Polynomial Rings ⋮ Binary Hermitian Lattices over Number Fields ⋮ On fast-decodable algebraic space-time codes ⋮ Natural construction of ten Borcherds-Kac-Moody algebras associated with elements in $M_{23}$ ⋮ Dual lattice of $\mathbb{Z}$-module lattice ⋮ A DETAILED STUDY OF THE RELATIONSHIP BETWEEN SOME OF THE ROOT LATTICES AND THE CODING THEORY ⋮ Attractive strings and five-branes, skew-holomorphic Jacobi forms and moonshine ⋮ Wiretap lattice codes from number fields with no small norm elements ⋮ A Hilbert irreducibility theorem for Enriques surfaces ⋮ Lattices in real quadratic fields and associated theta series arising from codes over ${\mathbb{F}}_4$ and ${\mathbb{F}}_2 \times {\mathbb{F}}_2$ ⋮ Spherical designs and heights of Euclidean lattices ⋮ Isomorphism theorem on vector spaces over a ring ⋮ Weighing matrices and spherical codes ⋮ Modular lattices from a variation of construction A over number fields ⋮ The work of Maryna Viazovska ⋮ Codes, vertex operators and topological modular forms ⋮ Automorphisms of extremal unimodular lattices in dimension 72 ⋮ From sphere packing to Fourier interpolation ⋮ Replicable functions arising from code-lattice VOAs fixed by automorphisms ⋮ Binary self-dual codes and Jacobi forms over a totally real subfield of $\mathbb{Q}(\zeta_8)$ ⋮ A note on construction of the Leech lattice ⋮ Revisiting lattice tiling decomposition and dithered quantisation ⋮ The magic of 8 and 24 ⋮ Analysis, geometry and topology of singular PDE. Abstracts from the workshop held June 6--12, 2021 (hybrid meeting) ⋮ On an Enriques Surface Associated With a Quartic Hessian Surface ⋮ Harder-Narasimhan theory for linear codes (with an appendix on Riemann-Roch theory) ⋮ A quadratic form approach to construction A of lattices over cyclic algebras ⋮ Automorphisms of modular lattices ⋮ Embedding theory of lattices and its application for $2$-integrable lattices ⋮ Low dimensional strongly perfect lattices. IV: The dual strongly perfect lattices of dimension 16 ⋮ Euclidean lattices, theta invariants, and thermodynamic formalism ⋮ Towards a ring analogue of the leftover hash lemma ⋮ Matrix of $\mathbb{Z}$-module ⋮ On Eisenstein polynomials and zeta polynomials II ⋮ Tutte polynomial, complete invariant, and theta series ⋮ Construction of Arakelov-modular lattices over totally definite quaternion algebras ⋮ Maximal discrete subgroups of 𝑆𝑂⁺(2,𝑛+2) ⋮ Algebraic lattices via polynomial rings ⋮ Universal optimality of the $E_8$ and Leech lattices and interpolation formulas ⋮ Vertex operator algebras with positive central charges whose dimensions of weight one spaces are 8 and 16 ⋮ Maximal digraphs whose Hermitian spectral radius is at most 2 ⋮ Torsion $\mathbb Z$-module and torsion-free $\mathbb Z$-module ⋮ On skew polynomial codes and lattices from quotients of cyclic division algebras