Construction of quantum BCH code based on cyclotomic coset - Lijuan XING; Zhuo LI (Tongxin xuebao)
Quantum-error-correcting code can overcome quantum decoherence efficiently, which is the key technology to realize quantum computers.A series of quantum BCH code was proposed based on classical codes.First, a general way of well-chosen cyclotomic coset was introduced.A sufficient condition was given to calculate the number of elements in cyclotomic coset.Then, a series of quantum BCH (Bose-Chaudhuri-Hocquenghem) code over finite field Fq was constructed by CSS (Calderbank-Shor-Steane) construction and Steane construction.The results were extended to finite field Fq2 with Hermitian construction.Compared with the results in literature,the range of introduced cyclotomic coset is more wide, and the new quantum BCH code has higher dimensions and better lower bounds on minimum distances.Furthermore, a family of quantum maximum distance separable (quantum MDS) code over any finite fields is constructed.