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One-Lee weight and two-Lee weight $\mathbb{Z}_2\mathbb{Z}_2[u]$-additive codes (1609.09588v3)
Published 30 Sep 2016 in math.RA, cs.IT, and math.IT
Abstract: In this paper, we study one-Lee weight and two-Lee weight codes over $\mathbb{Z}{2}\mathbb{Z}{2}[u]$, where $u{2}=0$. Some properties of one-Lee weight $\mathbb{Z}{2}\mathbb{Z}{2}[u]$-additive codes are given, and a complete classification of one-Lee weight $\mathbb{Z}2\mathbb{Z}_2[u]$-additive formally self-dual codes is obtained. The structure of two-Lee weight projective $\mathbb{Z}_2\mathbb{Z}_2[u]$ codes is determined. Some optimal binary linear codes are obtained directly from one-Lee weight and two-Lee weight $\mathbb{Z}{2}\mathbb{Z}_{2}[u]$-additive codes via the extended Gray map.