Constructions Of New Entangled-assisted Quantum MDS Codes From GRS Codes

With the further development of communication technology,quantum communication has become a hot issue in today’s research.Similar to classical communication,there still exists some problems of inaccuracy or missing information transmission in quantum communication as well as the coherence of quantum states.The theory of quantum error correction codes is particularly important in quantum communication.In the further study of quantum error correction codes,researchers found that by introducing the concept of quantum entangled state,entangled-assisted quantum error correction codes can be constructed from any classical codes.How to construct entangled-assisted quantum error correction codes is a very important problem.The main research of this thesis is constructing three kinds of entangled-assisted quantum MDS codes from GRS codes over finite fields.These codes have good properties in error correction.The first kind of entangled-assisted quantum error correction codes gives a construction which is different from the research by Lanqiang Li et al.in 2019.In their work,they constructed two kinds of entangled-assisted quantum error correction codes in the case of q=2am-1 and q=(2a+1)m-1.The result is in the case of q=sm+1.The second kind of entanglement-assisted quantum error correction codes is constructed from GRS codes obtained by tensor product based on vectors with lengths q+1/h and q-1.The third kind of entangled-assisted quantum error correction codes is based on the GRS code constructed by tensor product of prime factors decomposed by q2-1.This prime decomposition method used by Shuo Chen in constructing quantum error correction codes is applied to constructing entangled-assisted quantum error correction codes.The research of this thesis is helpful to the further study of entangled-assisted quantum error codes in the future.