One-Lee weight and two-Lee weight ℤ₂ℤ₂[u]-additive codes

2016/09/30 by Zhenliang Lu, Liqi Wang, Lu, Zhenliang +5
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Computer and information sciences #FOS: Mathematics #Finite Group Theory Research #Information Theory (cs.IT) #Rings and Algebras (math.RA) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1609.09588

openalex publication_date 2016/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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