Rank of the linear-representation incidence matrix over finite fields equals 1 plus (q minus 1) times the number of hyperplanes meeting K, and the corresponding LDPC code is generated by minimum-weight plane words.
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Linear representations of finite geometries and associated LDPC codes
Rank of the linear-representation incidence matrix over finite fields equals 1 plus (q minus 1) times the number of hyperplanes meeting K, and the corresponding LDPC code is generated by minimum-weight plane words.