  The analysis of the decoding failure rate of the bit-flipping algorithm has
received increasing attention. For a binary linear code we consider the minimum
number of rows in a parity-check matrix such that the bit-flipping algorithm is
able to correct errors up to the minimum distance without any decoding
failures. We initiate a study of this bit-flipping redundancy, which is akin to
the stopping set, trapping set or pseudocodeword redundancy of binary linear
codes, and focus in particular on codes based on finite geometries.
