Christine Kelley, University of Nebraska-Lincoln
Authors: Christine Kelley and Meraiah Martinez
2022 AWM Research Symposium
Women in Graph Theory and Applications

Reproducible parity check codes have parity check matrices that can be specified by a few rows along with a set of transformations on those rows. Some examples of reproducible codes include array-based LDPC codes with dyadic or $n$-adic matrices as blocks. When such a block has weight $j$, it can be viewed as a sum of $j$ permutation matrices. In this talk we examine how the structure of the permutations corresponding to the blocks can be used to obtain parameters of the overall code. We also consider other families of permutation matrices to construct new reproducible codes.

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