环 F2＋ uF2＋ u2 F2上的常循环码

摘要

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+ λu ) constacyclic codes with an arbitrary length N over the ring R= F2+ uF2+ u2 F2 are investigated ,where λis a unit of the ring R .Based on the analysis of the equivalence between 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 ob-tained ,so are the codes with length N≡2 (mod 4 ) .%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＋ uF2＋ u2 F2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。