English

One-Lee weight and two-Lee weight $\mathbb{Z}_2\mathbb{Z}_2[u]$-additive codes

Rings and Algebras 2018-02-05 v3 Information Theory math.IT

Abstract

In this paper, we study one-Lee weight and two-Lee weight codes over Z2Z2[u]\mathbb{Z}_{2}\mathbb{Z}_{2}[u], where u2=0u^{2}=0. Some properties of one-Lee weight Z2Z2[u]\mathbb{Z}_{2}\mathbb{Z}_{2}[u]-additive codes are given, and a complete classification of one-Lee weight Z2Z2[u]\mathbb{Z}_2\mathbb{Z}_2[u]-additive formally self-dual codes is obtained. The structure of two-Lee weight projective Z2Z2[u]\mathbb{Z}_2\mathbb{Z}_2[u] codes is determined. Some optimal binary linear codes are obtained directly from one-Lee weight and two-Lee weight Z2Z2[u]\mathbb{Z}_{2}\mathbb{Z}_{2}[u]-additive codes via the extended Gray map.

Keywords

Cite

@article{arxiv.1609.09588,
  title  = {One-Lee weight and two-Lee weight $\mathbb{Z}_2\mathbb{Z}_2[u]$-additive codes},
  author = {Zhenliang Lu and Liqi Wang and Shixin Zhu and Xiaoshan Kai},
  journal= {arXiv preprint arXiv:1609.09588},
  year   = {2018}
}
R2 v1 2026-06-22T16:06:11.310Z