Research Of (1+u)-constacyclic Codes Of Arbitrary Length Over A Kind Of Rings

In resent years, the theory of ring of coding and cryptography is the key for researcher in coding and cryptography. In particular, the study of code over the ring Fq[u]/(uk).We study (1+u)-constacyclic codes over the ring Fp+uFp.We give the defintion of (l+u)-constacyclic codes of an arbitrary length n over the ring Fp+uFp. We define a mapφ, which is from the arbitrary length (1+u)-constaclic code to the quotient rings. Through the mapφ, we give the structure and the classification of (l+u)-constacyclic codes of an arbitrary length n over the ring Fp+uFp. And we conclude by giving an example of (l+u)-constacyclic codes. We prove that the Gray image of any (l+u)-constacyclic codes which is a cyclic code of length pn. Furthermore, we discuss the dual codes of (1+u)-constacyclic codes. Finally, we study the Gray map of (1+u)-constacyclic codes.