Constructions Of Entanglement-assisted Quantum Error-correcting Codes From Skew Constacyclic Codes Over Finite Fields

Let Fq be a q=pm element finite field,we get the relationship that the dimension of the intersection of a θ-λ-cyclic code and its dual code is equal to the degree of the monic greatest right-hand common factor of the generator polynomial of the code and the generator polynomial of its dual code.By analyzing the properties of the monic largest right common factor and the monic least left common multiple of the polynomials in the Fq[x;θ]ring,the special properties of the intersection of the skew constacyclic code and its dual code are explored,that is,when λ≠±1,the intersection of the θ-λ-cyclic code C and its dual code is {0},and when λ1λ2≠1,the dimension of the same θ-λ1-cyclic code C1 andθ-λ2-cyclic codes C2 satisfy C1∩C1⊥={0｝,C2 ∩C1⊥={0}.Entanglement-assisted quantum error correction codes can be constructed by using non-symplectic-abelian linear codes,and by finding the isotropic generators and the pa.irs of hyperbolic generators on the non-symplectic-abelian linear code on Fq,we expand the non-symplectic-abelian subgroups into higherdimensional symplectic-abelian linear codes,and thus find the methods for constructing entanglement-assisted quantum error-correcting codes by non-symplecticself-orthogonal linear codes and their symplectic-dual codes and by a linear codes or two linear codes with the same length and their dual codes,and determine the relationship between the parameters of the linear codes and the entanglementassisted quantum error-correcting codes in the above methods.Using the properties of the intersection of the θ-λ-cyclic code and its dual code when λ≠±1 on Fq,and the properties of θ-λ1-cyclic code C1 and θ-λ2-cyclic code C2 the sa.me length and the condition λ1λ2≠1,the entanglement-assisted quantum errorcorrecting codes,including the entanglement-assisted quantum error-correcting codes with great entanglement,are constructed.