Abstract: Let R=F₂+uF₂+u²F₂，the depth of a codeword and the depth distribution of linear codes over ring R are defined，a number of properties of the depth of codewords are studied，and the recursive algorithm for computing the depth of a codeword is given.Based on the linear codes over R and their generator matrices，the linear codes C1,Cu,Cu2 over F2 and their generator matrices are obtained.By using the relationship of C1,Cu,Cu2，the depth distribution and the depth spectrum of linear codes over R are discussed，moreover the depth distribution of a class of linear code over R is showed.

Key words: linear code, generator matrix, depth distribution, depth spectrum

摘要： 记R=F₂+uF₂+u²F₂，定义了环R上码字的深度以及R上线性码的深度分布，研究了环R上码字深度的性质，给出了计算环[R]上码字深度的递归算法。利用环R上的线性码C及其生成矩阵，得到了域F2上的线性码C1,Cu,Cu2及相应的生成矩阵。通过域F2上的线性码C1,Cu,Cu2之间的关系，讨论了环R上的线性码的深度谱和深度分布，进而得到R上一类线性码的深度分布。

关键词: 线性码, 生成矩阵, 深度分布, 深度谱