On the Pless Construction and ML Decoding of the Quadratic Residue Code

We present a method for maximumlikelihood decoding of the quadratic residue code This method is based on projecting the code onto a subcode with an acyclic Tanner graph and representing the set of coset leaders by a trellis diagram This results in a two level coset decoding which can be considered a systematic generalization of the Wagner rule We show that unlike the Golay code the code does not have a Pless construction which has been an open question in the literature It is determined that the highest minimum distance of a binary code having a Pless construction is and up to equivalence there are three such codes