Research On Some Problems Of Codes Over The Ring F_p+vF_p

Cyclic codes over the finite chain rings has been widly researched. But there are some optimal codes over non-chain rings exactly, not considering the hardness of researching on it. Constacyclic code is a kind of good codes about error correct. This thesis has just worked on the structure and the image under the Gray map of the constacyclic codes over the non-chain ring Fp+vFp, with v2=1.First of all, The Gray map is defined from Fp+vFp to Fp.The image of such code under the defined Gray map is pointed out to be a distance invariant linear cyclic code of length2n over Fp, and the image of linear cyclic codes with odd length is explained to be some p-ary linear cyclic codes. The Gray image of the v-constacyclic code over Fp+vFp is structured by determining its generator polynomial. The structure of the Gray image of the dual code of the v-constacyclic code is investigated, and the generator is determined.Since some results on the v-constacyclic code over the ring Fp+vFp are actually special situations of the characteristics of any λ-constacyclic code. To be continued, the identity λ=α+vβ in Fp+vFp is drawed in, and the λ-constacyclic code over Fp+vFp is structured. The generator polynomial of the λ-constacyclic code is determined, and the generating set in standard form is defined. All of the constacyclic codes over Fp+vFp are principally generated. The Gray image and the dual codes of all λ-constacyclic codes are described. The structure of the Gray image of the dual code is analyzed, and the generator is given.