Coded modulation based on rings of integers modulo-q. 1. Block codes

The authors aim to present an alternative multilevel (nonbinary) coding method, based on a ring of integers modulo-q (q is a nonprime integer number) which is suitable for coded modulation schemes. Some new concepts and definitions are introduced in order to build up a theoretical framework which allows a search for good multilevel codes. Such classes of block codes are also presented together with their interesting properties. Such codes can be used not only in q-PSK modulations, but also in q-QAM modulations by making a simple adaptation