EISENSTEIN LATTICES, GALOIS RINGS AND QUATERNARY CODES
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Publication:5483368
DOI10.1142/S1793042106000577zbMath1127.11048OpenAlexW2037659346MaRDI QIDQ5483368
Ann Marie Natividad, Patrick Solé, Philippe Gaborit
Publication date: 14 August 2006
Published in: International Journal of Number Theory (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1142/s1793042106000577
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Cites Work
- The shadow theory of modular and unimodular lattices
- Applications of coding theory to the construction of modular lattices
- On the algebraic structure of quasi-cyclic codes. II: Chain rings
- Eisenstein lattices, Galois rings, and theta series.
- Quadratic double circulant codes over fields
- Type II codes over \(\mathbb F_4\)
- Jacobi forms over totally real fields and type II codes over Galois rings \(\operatorname{GR}(2^{m},f)\).
- Construction of new extremal unimodular lattices
- The Z/sub 4/-linearity of Kerdock, Preparata, Goethals, and related codes
- All self-dual Z/sub 4/ codes of length 15 or less are known
- Quaternary quadratic residue codes and unimodular lattices
