Difference set codes: codes with squared Euclidean distance of six for partial response channels

We present a new construction of block codes for the (1-D)-PR (partial response) channel. The codewords in the code correspond to constant-sum subsets of a difference set. It is shown that at the output of a noiseless (1-D)-PR channel; the minimum squared Euclidean distance of such a code is at least six, compared to two for the uncoded system. This construction yields larger code rates than previously known codes with the same minimum distance for large code lengths. The construction technique also imposes upper bounds on the decoding complexity of the codes