, Volume 11, Issue 1, pp 359-391

Cube-tilings of ℝ n and nonlinear codesand nonlinear codes

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Abstract

Families of nonlattice tilings of ℝ n 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 ℝ n such that no two cubes have a common face of dimension exceeding \(n - \tfrac{1}{3}\sqrt n\) .