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
Parents
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
Page edit log
- Victor V. Albert (2025-03-26) — most recent
Cite as:
“Harada-Kitazume code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/harada_kitazume