A method is disclosed for encoding and modulating bits of an information stream and transmitting them over a designated channel in a high speed communication system. The method includes the steps of dividing a set of the entire constellation of available points into a finite plurality of zero parity vectors defined by two criteria, namely that (1) the column vectors have odd parity and (2) a group of a predefined integer number of column vectors have a 0 modulus (i.e. be divisible by a given number). Column vectors forming only a partially dimensioned portion of the code (e.g. 4D) corresponding to one discrete baud interval are preferably transmitted in a systematic form and with sufficient coding gain for adaptive DFE equalization and whereby a group of column vectors corresponding to an integer number of successive baud intervals that form the fully dimensioned code (e.g. 16D) are transmitted with correlation to one another to achieve an even greater amount of coding gain suitable for high reliability data transmission with error correction and subsequent detection that yield a low bit error rate.