Nonexistence of face-to-face four-dimensional tilings in the Lee metric

DOI10.1016/j.ejc.2005.08.003zbMath1109.52015OpenAlexW1997293718MaRDI QIDQ854814

Simon Špacapan

Publication date: 7 December 2006

Published in: European Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ejc.2005.08.003

zbMATH Keywords

tilingLee spheres

Mathematics Subject Classification ID

Combinatorics in computer science (68R05) Combinatorial aspects of tessellation and tiling problems (05B45) Tilings in (n) dimensions (aspects of discrete geometry) (52C22) Mathematical programming (90C99)

Related Items (11)

A new approach towards the Golomb-Welch conjecture ⋮ Restriction conditions on \(\mathrm{PL}(7, 2)\) codes \((3 \le \vert\mathcal{G}_i\vert \le 7)\) ⋮ On linear diameter perfect Lee codes with distance 6 ⋮ On the nonexistence of lattice tilings of \(\mathbb{Z}^n\) by Lee spheres ⋮ Non-periodic tilings of \({\mathbb{R}}^{n}\) by crosses ⋮ On the non-existence of linear perfect Lee codes: the Zhang-Ge condition and a new polynomial criterion ⋮ The structure of cube tilings under symmetry conditions ⋮ Tilings in Lee metric ⋮ On perfect Lee codes ⋮ Perfect codes in the discrete simplex ⋮ Nonexistence of perfect 2-error-correcting Lee codes in certain dimensions

Cites Work

• Unnamed Item
• On the asymptotic behaviour of Lee-codes
• On the non-existence of 3-dimensional tiling in the Lee metric
• An Elias-type bound for Lee codes over large alphabets and its application to perfect codes (Corresp.)
• Nonexistence theorems on perfect Lee codes over large alphabets
• Perfect Codes in the Lee Metric and the Packing of Polyominoes

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