The Preparata and Goethals codes: trellis complexity and twisted squaring constructions

The trellis complexity of the Preparata and Goethals codes is examined. It is shown that at least for a given set of permutations these codes are rectangular. Upper bounds on the state complexity profiles of the Preparata and Goethals codes are given. The upper bounds on the state complexity of the Preparata and Goethals codes are determined by the dimension/length profiles (DLP) of the extended primitive double- and triple-error-correcting BCH codes, respectively. A twisted squaring construction for the Preparata and Goethals codes is given, based on the double- and triple-error-correcting extended primitive BCH codes, respectively.