Quantum Codes From Constacyclic Codes Over Finite Rings

Because of the application in quantum computation and quantum communication,quantum codes have attracted many scholars’ attention.Many scholars construct quantum codes by using self-orthogonal linear codes.In recent years,it has become the new research focus to construct quantum codes with excellent parameters based on the constacyclic codes over rings.This dissertation mainly study the following contents:(1)We study the properties of(1-2μ-2v)-constacyclic codes over the finite non-chain ring R=Fq+uFq+vFq and give a new Gray map from the ring R=Fq+uFq+vFq to the field Fq with the property that it can preserve the code-distance and self-orthogonality.(2)Some new quantum codes are constructed by constructing self-orthogonal constacyclic codes over the ring R=Fq+uFq+vFq.(3)Based on the study of the(1-2v)-constacyclic codes over the finite non-chain ring R=Fp+vFp in[37],a new Gray map from the ring R=Fp+vFp to the field Fq is given and it can preserve the code-distance and self-orthogonality.Finally some quantum codes with new parameters are constructed.