Agnarsson, GeirFarinholt, Jacob M.2012-10-05NO_RESTRIC2012-10-052012-10-05https://hdl.handle.net/1920/7947Due to their fast decoding algorithms, quantum generalizations of low-density parity check, or LDPC, codes have been invesitgated as a solution to the problem of decoherence in fragile quantum states [1, 2]. However, the additional twisted inner product requirements of quantum stabilizer codes force four-cycles and eliminate the possibility of randomly generated quantum LDPC codes. Moreover, the classes of quantum LDPC codes discovered thus far generally have unknown or small minimum distance, or a fixed rate (see [3, 4] and references therin). This paper presents several new classes of quantum LDPC codes constructed from finite projective planes. These codes have rates that increase with the block length n and minimum weights proportional to n1=2. For the sake of completeness, we include an introduction to classical error correction and LDPC codes, and provide a review of quantum communication, quantum stabilizer codes, and finite projective geometry.enQuantum error correctionError correcting codesFinite geometryThesis