A DETAILED STUDY OF THE RELATIONSHIP BETWEEN SOME OF THE ROOT LATTICES AND THE CODING THEORY

DOI10.2206/kyushujm.72.123zbMath1429.11119OpenAlexW2810892555MaRDI QIDQ4577891

Michio Ozeki

Publication date: 3 August 2018

Published in: Kyushu Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2206/kyushujm.72.123

zbMATH Keywords

coding theoryunimodular latticeroot lattice

Mathematics Subject Classification ID

Lattices and convex bodies (number-theoretic aspects) (11H06) Relations with coding theory (11H71)

Uses Software

• Magma

Cites Work

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• On the classification of integral even unimodular 24-dimensional quadratic forms
• Self-dual codes over GF(5)
• On the enumeration of lattices of determinant one
• Self-dual codes over the integers modulo 4
• Upper bounds for modular forms, lattices, and codes
• Niemeier lattices and Type II codes over \(\mathbb{Z}_4\)
• Unimodular lattices with a complete root system
• A new construction of lattices from codes over GF(3)
• All \(\mathbb{Z}_ 4\) codes of type II and length 16 are known
• The Magma algebra system. I: The user language
• A classification of self-orthogonal codes over GF(2)
• Definite quadratische Formen der Dimension 24 und Diskriminante 1
• Spiegelungsgruppen und Aufzählung halbeinfacher Liescher Ringe
• Lattices and Codes
• On the Classification of Type II Codes of Length 24
• Self-Dual Codes over ${\text{GF}}( 3 )$
• Self-dual codes over<tex>GF(3)</tex>and<tex>GF(4)</tex>of length not exceeding 16
• Notes on Sphere Packings
• On the uniqueness of the Golay codes
• Sphere Packings and Error-Correcting Codes
• On the classification and enumeration of self-dual codes

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