| BCH codes are the source of constructing quantum codes with better parameters in finite fields,In this paper,two classes of BCH codes are constructed,and according to the Hermittian dual,two classes of quantum codes with better performance are also constructed.The specific results are as follows:1.The classical BCH codes are used to construct quantum BCH codes.While n=r(q~2-1),m=ord_n(q ~2)=4,the distribution characteristics of elements in q~2mod n partitioned cyclotomic cosets and the conditions for selecting the disjoint of specific set are analyzed.Based on the construction theory of BCH code,a new class of BCH code is constructed.According to Hermittian constructions,some quantum codes with new parameters are constructed in this paper.Compared with the existing quantum code literature,the performance of the quantum code constructed in this paper is a little better,mainly reflected in the aspects of large dimension and high rate.2.The constacyclic quantum codes are constructed by using constacyclic BCH codes.While n=λ(q~2+1),λ∣q-1,1≤λ≤(q-1)/2,the distribution characteristics of the head of q~2mod(q+1)n cyclotomic cosets are analyzed,according to the construction method of constacyclic codes,a new class of constacyclic codes of code length is constructed.According to Hermittian constructions,some quantum codes are constructed in this paper.Compared with some existing quantum codes,the quantum codes constructed in this paper not only have good performance,but also construct some quantum codes with new parameters. |
