Perfect codes in the \(\ell_p\) metric

DOI10.1016/j.ejc.2015.11.002zbMath1330.94064arXiv1506.02517OpenAlexW578426344MaRDI QIDQ901156

Antonio Campello, Grasiele C. Jorge, Sueli I. R. Costa, João Eloir Strapasson

Publication date: 23 December 2015

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

Full work available at URL: https://arxiv.org/abs/1506.02517

Mathematics Subject Classification ID

Other types of codes (94B60) Applications of the theory of convex sets and geometry of numbers (covering radius, etc.) to coding theory (94B75)

Related Items (6)

On the structure of cube tiling codes ⋮ Gluing and cutting cube tiling codes in dimension six ⋮ Perfect codes in Euclidean lattices ⋮ Bounds for the \(l_1\)-distance of \(q\)-ary lattices obtained via constructions \(\mathrm D\), \(\mathrm D'\) and \(\overline{\mathrm D}\) ⋮ On the non-existence of linear perfect Lee codes: the Zhang-Ge condition and a new polynomial criterion ⋮ Quasi-perfect codes in the \(\ell _p\) metric

Cites Work

• Fast decoding of quasi-perfect Lee distance codes
• A note on optimal unimodular lattices
• New upper bounds on sphere packings. I
• Constructive spherical codes near the Shannon bound
• On the non-existence of lattice tilings by quasi-crosses
• A new approach towards the Golomb-Welch conjecture
• An improvement to the Minkowski‐Hiawka bound for packing superballs
• Quasi-Cross Lattice Tilings With Applications to Flash Memory
• Perfect Codes in the Lee Metric and the Packing of Polyominoes
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