环Fp+vFp上互补对偶常循环码

摘要

In this paper, we investigate the complementary-dual (1?2v)-constacyclic codes over the ring Fp+vFp(v2=v), where p is a prime. Using the decomposition C =vC1?v⊕(1?v)Cv of a (1?2v)-constacyclic code over Fp+vFp, we obtain generator polynomial of the complementary-dual (1?2v)-constacyclic code C. Then by means of the Gray map from Fp+vFp to F2p, we show that Gray images of complementary-dual (1?2v)-constacyclic codes over Fp+vFp are complementary-dual cyclic codes over Fp.%本文研究了环Fp+vFp上互补对偶(1?2v)-常循环码.利用环Fp+vFp上(1?2v)-常循环码的分解式C=vC1?v⊕(1?v)Cv,得到了环Fp+vFp上互补对偶(1?2v)-常循环码的生成多项式.然后借助从Fp+vFp到F 2p的Gray映射,证明了环Fp+vFp上互补对偶(1?2v)-常循环码的Gray像是Fp的互补对偶循环码.