Unique and Minimum Distance Decoding of Linear Codes with Reduced Complexity

We show that for (systematic) linear codes the time complexity of unique decoding is O(n^{2}q^{nRH(delta/2/R)}) and the time complexity of minimum distance decoding is O(n^{2}q^{nRH(delta/R)}). The proposed algorithm inspects all error patterns in the information set of the received message of weight less than d/2 or d, respectively.