A set of quantum error-correcting codes based on classical Reed-Muller codes is described. The codes have parameters [[n,k,d]]=[[2/sup r/,s/sup r/-C(r,t)-2/spl Sigma//sub i=0//sup t-1/C(r,i),2/sup t/+2/sup t-1/]].
In this thesis, we start from the theory of classical error-correcting codes. We also introduce classical Reed-Muller codes along with its properties. We discuss the encoding and decoding methods for classical Reed-Muller codes using the majority rule. Then we turn to the topic of quantum error-correcting codes.We talk about stabilizer codes and discuss how classical Reed-Muller codes can be transformed into quantum Reed-Muller codes using Steane's method. Finally, we give a construction of a quantum code with parameter [[8,3,3]], and discuss its encoding and decoding process.