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Description
Dyadic matrices are a subclass of matrices known as reproducible matrices, where the entries of the matrix are completely determined by their first row. Quasi-dyadic matrices are block matrices with dyadic matrices in the blocks.
There has been extensive work analyzing quasi-cyclic codes, codes defined by quasi-cyclic parity check matrices, but less is known about codes arising from dyadic or quasi-dyadic matrices. In this work, we present results on the properties of the Tanner graphs of dyadic and quasi-dyadic codes. In particular, we present results on their isomorphism classes, absorbing sets, and conditions for constructing quasi-dyadic matrices with Tanner graphs of a certain girth. We also compare the performance of these code constructions under Belief Propagation decoding.