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This paper is concerned with construction and structural analysis of bothcyclic and quasi-cyclic codes, particularly LDPC codes. It consists of threeparts. The first part shows that a cyclic code given by a parity-check matrixin circulant form can be decomposed into descendant cyclic and quasi-cycliccodes of various lengths and rates. Some fundamental structural properties ofthese descendant codes are developed, including the characterizations of theroots of the generator polynomial of a cyclic descendant code. The second partof the paper shows that cyclic and quasi-cyclic descendant LDPC codes can bederived from cyclic finite geometry LDPC codes using the results developed infirst part of the paper. This enlarges the repertoire of cyclic LDPC codes. Thethird part of the paper analyzes the trapping sets of regular LDPC codes whoseparity-check matrices satisfy a certain constraint on their rows and columns.Several classes of finite geometry and finite field cyclic and quasi-cyclicLDPC codes with large minimum weights are shown to have no harmful trappingsets with size smaller than their minimum weights. Consequently, theirperformance error-floors are dominated by their minimum weights.

Cyclic and Quasi-Cyclic LDPC Codes on Row and Column Constrained Parity-Check Matrices and Their Trapping Sets