| 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. |
