Linear Generalized Preparata Codes over ℤ2s and a SISO MAP Decoding Algorithm for Them

In this paper, we introduce a SISO MAP decoding algorithm for the duals of the generalized Kerdock codes (a class of low-rate linear block codes over the $\mathbb{Z}_{2}s$ ring), which we refer to as the generalized Preparata codes. The decoding complexity of this algorithm is $O(N^{S}\log_{2}N)$ (where N is the code length in $\mathbb{Z}_{2}s$), which is significantly lower than the exhaustive search MAP decoder or the classical ML decoder implemented as a minimum distance or maximum correlation decoder.