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Harada-Kitazume code[1]

Description

A member of a family of extremal Type II self-dual codes over \(\mathbb{Z}_4\) that yield all Niemeier lattices via Construction \(A_4\).

Cousins

  • Niemeier lattice— Niemeier lattices can be constructed from quaternary codes over \(\mathbb{Z}_4\) via Construction \(A_4\) [2]. These codes are the Harada-Kitazume codes [1].
  • Self-dual linear code— Codewords consisting of 0 and 2 of nine Harada-Kitazume codes are of the form \(2c\), where \(c\) is a codeword of one of the nine corresponding \([24,12]\) doubly even self-dual codes [1].

Member of code lists

Primary Hierarchy

Classical Domain
Ring Kingdom
Ring codeECC
\(q\)-ary code over \(\mathbb{Z}_q\)ECC
Linear code over \(\mathbb{Z}_q\)ECC
Linear code over \(\mathbb{Z}_4\)
Dual code over \(\mathbb{Z}_4\)Linear code over \(\mathbb{Z}_q\) ECC
Self-dual code over \(\mathbb{Z}_4\)Linear code over \(\mathbb{Z}_q\) ECC
Parents
Self-dual code over \(\mathbb{Z}_4\)
Harada-Kitazume codes are extremal Type II self-dual codes over \(\mathbb{Z}_4\) [1].
Harada-Kitazume code

References

[1]
M. Harada and M. Kitazume, “Z4-Code Constructions for the Niemeier Lattices and their Embeddings in the Leech Lattice”, European Journal of Combinatorics 21, 473 (2000) DOI
[2]
A. Bonnecaze, P. Gaborit, M. Harada, M. Kitazume, and P. Solé, “Niemeier lattices and Type II codes over Z4”, Discrete Mathematics 205, 1 (1999) DOI
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Zoo Code ID: harada_kitazume

Cite as:
“Harada-Kitazume code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/harada_kitazume, arXiv:2606.11484
BibTeX:
@incollection{eczoo_harada_kitazume,
title={Harada-Kitazume code},
booktitle={The Error Correction Zoo},
year={2026},
editor={Albert, Victor V. and Faist, Philippe},
eprint={2606.11484},
doi={10.48550/arXiv.2606.11484},
url={https://errorcorrectionzoo.org/c/harada_kitazume}
}
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Permanent link:
https://errorcorrectionzoo.org/c/harada_kitazume

Cite as:

“Harada-Kitazume code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/harada_kitazume, arXiv:2606.11484

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/rings/over_zq/over_z4/linear_over_z4/self_dual/harada_kitazume.yml.