A New Algorithm for Finding Minimum-Weight Words in a Linear Code: Application to McEliece's Cryptosystem and to Narrow-Sense BCH Codes of Length 511

367 followed by addition which is completed in one clock unit time. The DFT is computed using a systolic cell described in [15]. For IBA-1 and IBA-2 the computation of the common connection polynomial is done by processing rows or columns serially. The computations of the connection polynomials for individual rows or columns in the case of Blahut's 2-D burst error correction are done concurrently. Except for the MSTD, the B-M algorithm works in the spectral domain. For the MSTD, the time-domain B-M algorithm is employed and in this case all computations of the B-M algorithm for rows or columns are done concurrently. To simplify the matters, conjugacy constraints and fast computation algorithms for DFT are not taken into account. Table I shows the complexity comparison. Both IBA-1 and IBA-2 show improvements in computational savings and decoding delay over BA-1 and BA-2, respectively. Relative improvement in the case of IBA-1 is more apparent compared to the improvement in the case of IBA-2. The IBA-1 has the smallest delay of all and the least hardware requirement. Since the IBA-1 requires simple control circuitry, it is preferable for small values of t and n. The IBA-2 has the smallest number of computations of all and marginally higher delay than the IBA-1. Hardware complexity of the IBA-2 is greater compared to the IBA-1. Therefore, the IBA-2 is preferable for large values of t and n. The MSTD has a larger number of computations compared to the IBA-2 and the longest delay of all. The MSTD may be used for moderate values of t and n, if the decoding delay is not stringent. It is to be noted that as the MSTD has to do 1-D DFT computation of either all the rows or columns, the time-domain implementation of the B-M algorithm for 2-D BCH decoding is not as advantageous as the time-domain implementation in the 1-D case. X. CONCLUSIONS We have presented deconvolution viewpoint for studying DFT domain decoding algorithms and applied it to obtain an alternative exposition of decoding algorithms for 2-D BCH codes. Some modifications to efficiently implement Blahut's decoding algorithm for 2-D BCH codes are suggested. It is shown that the modified algorithm requires at most half the number of passes compared to Blahut's original decoding algorithm. Improved versions of Blahut's decoding algorithms are given for correction of random and burst errors. Error-correcting capability of the class of 2-D BCH …