Double circulant codes over \(\mathbb{Z}_ 4\) and even unimodular lattices

DOI10.1023/A:1008639004036zbMath0881.94026OpenAlexW172261581MaRDI QIDQ679085

N. J. A. Sloane, Robert Calderbank

Publication date: 19 February 1998

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

Full work available at URL: https://doi.org/10.1023/a:1008639004036

zbMATH Keywords

40-dimensional unimodular latticedouble circulant codes over \(\mathbb{Z}_ 4\)even unimodular latticesself-dual codes over \(\mathbb{Z}_ 4\)

Mathematics Subject Classification ID

Lattice packing and covering (number-theoretic aspects) (11H31) Combinatorial codes (94B25) Combinatorial aspects of packing and covering (05B40)

Related Items (18)

An explicit expression for Euclidean self-dual cyclic codes of length \(2^k\) over Galois ring \(\mathrm{GR}(4,m)\) ⋮ Self-dual cyclic codes over \(\mathbb{Z}_4\) of length \(4n\) ⋮ An upper bound on the minimum weight of type II \(\mathbb Z_{2k}\)-codes ⋮ Linear codes and cyclic codes over finite rings and their generalizations: a survey ⋮ Construction of extremal type II \(\mathbb{Z}_{2 k}\)-codes ⋮ On the residue codes of extremal Type II \(\mathbb Z_4\)-codes of lengths 32 and 40 ⋮ Type IV-II codes over Z4 constructed from generalized bent functions ⋮ Residue codes of extremal type II \(\mathbb Z_4\)-codes and the moonshine vertex operator algebra ⋮ Universal codes and unimodular lattices ⋮ Extremal type II \(\mathbb{Z}_4\)-codes constructed from binary doubly even self-dual codes of length 40 ⋮ On the classification and enumeration of self-dual codes ⋮ \(\mathbb{Z}_4\)-code constructions for the Niemeier lattices and their embeddings in the Leech lattice ⋮ Construction of new extremal unimodular lattices ⋮ A 40-dimensional extremal type II lattice with no 4-frames ⋮ Extremal double circulant type II codes over \(\mathbb Z_4\) and construction of 5-(24,10,36) designs. ⋮ On the construction of self-dual cyclic codes over \(\mathbb{Z}_4\) with arbitrary even length ⋮ Niemeier lattices and Type II codes over \(\mathbb{Z}_4\) ⋮ Type II self-dual codes over finite rings and even unimodular lattices

Uses Software

• Magma

Cites Work

• Selbstduale Codes über dem Ring der ganzen Zahlen modulo 4. (Self-dual codes over the ring of integers modulo 4)
• The binary self-dual codes of length up to 32: A revised enumeration
• Self-dual codes over the integers modulo 4
• Jacobi polynomials, type II codes, and designs.
• Modular and \(p\)-adic cyclic codes
• Twenty-three constructions for the Leech lattice
• Error-Correcting Codes and Invariant Theory: New Applications of a Nineteenth-Century Technique
• The Z/sub 4/-linearity of Kerdock, Preparata, Goethals, and related codes
• Quaternary quadratic residue codes and unimodular lattices
• Finite Unitary Reflection Groups
• On the classification and enumeration of self-dual codes
• Algorithms in invariant theory
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