文章将有限域上关于Hamming重量的前3个 Pless 恒等式推 广到 $\mathbb{Z}_p\mathbb{Z}_p[u]$-加性码,其中 $p$ 是奇素数. 并利 用这些恒等式得到 $2$-Lee 重量 $\mathbb{Z}_p\mathbb{Z}_p[u]$-仿射加性码的存在条件. 最后给出若干 $2$-Lee 重量 $\mathbb{Z}_p\mathbb{Z}_p[u]$-加性码的构造.

In this paper, we generalize the first three Pless identities over finite fields on Hamming weights to the classes over $\mathbb{Z}_p\mathbb{Z}_p[u]$ on Lee weight, where $p$ is an odd prime number. Some existence conditions of two-Lee weight $\mathbb{Z}_p\mathbb{Z}_p[u]$-projective additive codes are discussed. Additionally, we describe some constructions of two-Lee weight $\mathbb{Z}_p\mathbb{Z}_p[u]$-additive codes.