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The state diagrams of a class of singular linear feedback shift registers(LFSR) are discussed. It is shown that the state diagrams of the given LFSRhave special structures. An algorithm is presented to construct a new class ofde Bruijn cycles from the state diagrams of these singular LFSR.

State Diagrams of a Class of Singular LFSR and Their Applications to the Construction of de Bruijn Cycles