Cube-tilings of \(\mathbb{R}^ n\) and nonlinear codes

DOI10.1007/BF02574014zbMath0804.52013OpenAlexW2020379838WikidataQ56699791 ScholiaQ56699791MaRDI QIDQ1329187

Jeffrey C. Lagarias, Peter W. Shor

Publication date: 29 June 1994

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/131307

zbMATH Keywords

nonlinear codesperfect codescube tilings

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Combinatorial aspects of tessellation and tiling problems (05B45) Theory of error-correcting codes and error-detecting codes (94B99) Tilings in (n) dimensions (aspects of discrete geometry) (52C22)

Related Items

Towards resolving Keller's cube tiling conjecture in dimension seven ⋮ Cube packings, second moment and holes ⋮ Partitions and balanced matchings of an \(n\)-dimensional cube ⋮ On the structure of cube tiling codes ⋮ Gluing and cutting cube tiling codes in dimension six ⋮ Irreducible subcube partitions ⋮ Rigidity and the chessboard theorem for cube packings ⋮ Rigid polyboxes and Keller's conjecture ⋮ On Keller's conjecture in dimension seven ⋮ Polyboxes, cube tilings and rigidity ⋮ What is known about unit cubes ⋮ The structure of cube tilings under symmetry conditions ⋮ Distinguishability of complete and unextendible product bases ⋮ Iterated function systems, Ruelle operators, and invariant projective measures

Cites Work

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• A combinatorial approach for Keller's conjecture
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• Über einfache und mehrfache Bedeckung des \(n\)-dimensionalen Raumes mit einem Würfelgitter
• Keller’s cube-tiling conjecture is false in high dimensions
• Algebraic Tiling
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