A Class Of Constacyclic BCH Codes And Its Application To Quantum Codes

BCH codes are an important class of cyclic codes with efficient encoding and decoding algorithms,so they have widely applications.Constacyclic BCH codes are the development and generalization of BCH codes,they have more flexible parameters and good algebraic structures.Constacyclic BCH codes can be used to construct quantum error correcting codes with good parameters.In this paper,we mainly study a class ofλ-constacyclic BCH codes over the finite field Fq2 with length n=q2m-1/[r(q-1)],and we use these constacyclic BCH codes to construct some quantum codes with good parameters,where ord(λ)=r,r|(q+1)and q is a prime power.Specific research contents are as follows:一、The structures of q2 cyclotomic cosets modulo nr are studied according to the parity of m,the maximum design distance of this class of constacyclic BCH codes to be Hermitian dual-containing codes are given,the dimensions of these Hermitian dual-containing constacyclic BCH codes are determined,and some quantum constacyclic BCH codes are obtained by using Hermitian construction,they have larger dimensions than the quantum BCH codes at the same lengths and design distances.二、For m≥3 and m is odd,the number of entangled state is calcuated by decomposing the defining set of this class of constacyclic BCH codes,and a class of entanglement-assisted quantum codes is constructed by using the construction method of entanglement-assisted quantum codes.