Some Families Of Quantum BCH Codes

Classical Bose-Chaudhuri-Hocquenghem(BCH)codes over finite fields have been studied extensively.Calderbank-Shor-Steane(CSS)construction,Steane’s enlargement construction and Hermitian construction produce quantum codes from classical codes.The BCH codes containing their Euclidean dual or Hermitian dual codes can be applied to construct good stabilizer codes.Therefore,we can construct quantum codes by classical BCH codes over finite fields in this thesis.Firstly,we study the properties of classical BCH codes in terms of cyclotomic cosets.It is convenient to compute the dimension of quantum BCH codes by mutually disjoint cyclotomic cosets.Meanwhile,it ensures that classical BCH codes are Euclidean dual-containing or Hermitian dual-containing so that we can construct several new families of quantum BCH codes.