基于（xn －1）在 F2[x]上的分解，研究了环 R＝ F2＋ uF2＋ u2 F2上任意长度的（1＋ u）常循环码的秩和极小生成元集，定义了环 R到F42的一个新的Gray映射，确定了环 R上任意长度的（1＋u）常循环码的Gray象的结构及Gray象的生成多项式，得到了一些最优的二元线性循环码。%In view of the factorization of (xn -1) in F2 [x] ,the minimal generating set and rank of (1+ u)‐constacyclic codes with an arbitrary length over the ring R= F2 + uF2 + u2 F2 were studied .A new Gray map from R to F42 was defined ,the structures and generator polynomials of the Gray image of a linear (1+ u)‐constacyclic code with an arbitrary length were determined ,and some optimal binary linear cyclic codes were obtained .
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