Graphs, Tessellations, and Perfect Codes on Flat Tori

DOI10.1109/TIT.2004.834754zbMath1231.94070OpenAlexW2137836566MaRDI QIDQ3546734

Reginaldo jun. Palazzo, Edson Agustini, Sueli I. R. Costa, Marcelo Muniz Silva Alves

Publication date: 21 December 2008

Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1109/tit.2004.834754

Mathematics Subject Classification ID

Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Cyclic codes (94B15)

Related Items (13)

A new approach towards the Golomb-Welch conjecture ⋮ Commutative group codes in \(\mathbb R^4\), \(\mathbb R^6\), \(\mathbb R^8\) and \(\mathbb R^{16}\)-approaching the bound ⋮ On the construction of new toric quantum codes and quantum burst-error-correcting codes ⋮ A note on suborthogonal lattices ⋮ A generalization of Lee codes ⋮ Codes over graphs derived from quotient rings of the quaternion orders ⋮ Lattice-like total perfect codes ⋮ Perfect codes in Euclidean lattices ⋮ On the construction and labelling of geometrically uniform signal sets in \(\mathbb R^{2}\) matched to additive quotient groups ⋮ Modeling hexagonal constellations with Eisenstein-Jacobi graphs ⋮ Flat tori, lattices and bounds for commutative group codes ⋮ Variational networks of cube-connected cycles are recursive cubes of rings ⋮ Circulant graphs and tessellations on flat tori

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