ThislettergivesarandomconstructionforLowDensityParityCheck(LDPC)codes,whichusesaniterativealgorithmtoavoidshortcyclesintheTannergraph.TheconstructionmethodhasgreatflexiblechoiceinLDPCcode'sparametersincludingcodelength,coderate,theleastgirthofthegraph,theweightofcolumnandrowintheparitycheckmatrix.ThemethodcanbeappliedtotheirregularLDPCcodesandstrictregularLDPCcodes.Systemiccodeshavemanyapplicationsindigitalcommunication,sothisletterproposesaconstructionofthegeneratormatrixofsystemicLDPCcodesfromtheparitycheckmatrix.Simulationsshowthatthemethodperformswellwithiterativedecoding.