Discrete & Computational Geometry

, Volume 11, Issue 4, pp 359–391

Cube-tilings of ℝn and nonlinear codesand nonlinear codes

  • J. C. Lagarias
  • P. W. Shor

DOI: 10.1007/BF02574014

Cite this article as:
Lagarias, J.C. & Shor, P.W. Discrete Comput Geom (1994) 11: 359. doi:10.1007/BF02574014


Families of nonlattice tilings of ℝn by unit cubes are constructed. These tilings are specializations of certain families of nonlinear codes overGF(2). These cube-tilings provide building blocks for the construction of cube-tilings such that no two cubes have a high-dimensional face in common. We construct cube-tilings of ℝn such that no two cubes have a common face of dimension exceeding\(n - \tfrac{1}{3}\sqrt n\).

Copyright information

© Springer-Verlag New York Inc. 1994

Authors and Affiliations

  • J. C. Lagarias
    • 1
  • P. W. Shor
    • 1
  1. 1.AT&T Bell LaboratoriesMurray HillUSA

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