环F_2+uF_2+u^2F_2上的常循环码

Constacyclic Codes over the Ring F_2+ uF_2+ u^2F_2

常循环码是一类重要的纠错码,本文基于(xn-1)在F2[x]上的分解,探讨了环R=F2+u F2+u2F2上任意长度的(1+λu)常循环码的极小生成元集(λ为R上的单位).通过分析该环上循环码和常循环码的置换等价性,得到了该环上码长为奇数及码长N≡2(mod 4)时(1+u2)常循环码的生成多项式和极小生成元集.

Constacyclic codes are a kind of important error-correcting codes. In view of the factorization of（ xn- 1）in F2[x],the minimal generating set of（ 1 ＋ λ u） constacyclic codes with an arbitrary length N over the ring R = F2＋ uF2＋ u2F2 are investigated,w here λ is a unit of the ring R. Based on the analysis of the equivalence betw een cyclic codes and constacyclic codes over the ring R,the generator polynomials and minimal generating set of（ 1 ＋ u2） constacyclic codes with odd length are obtained,so are the codes w ith length N≡2（ mod 4）.