  This paper addresses the blind recovery of the parity check matrix of an
(n,k) linear block code over noisy channels by proposing a fast recovery scheme
consisting of 3 parts. Firstly, this scheme performs initial error position
detection among the received codewords and selects the desirable codewords.
Then, this scheme conducts Gaussian elimination (GE) on a k-by-k full-rank
matrix and uses a threshold and the reliability associated to verify the
recovered dual words, aiming to improve the reliability of recovery. Finally,
it performs decoding on the received codewords with partially recovered dual
words. These three parts can be combined into different schemes for different
noise level scenarios. The GEV that combines Gaussian elimination and
verification has a significantly lower recovery failure probability and a much
lower computational complexity than an existing Canteaut-Chabaud-based
algorithm, which relies on GE on n-by-n full-rank matrices. The decoding-aided
recovery (DAR) and error-detection-&-codeword-selection-&-decoding-aided
recovery (EDCSDAR) schemes can improve the code recovery performance over GEV
for high noise level scenarios, and their computational complexities remain
much lower than the Canteaut-Chabaud-based algorithm.
