Weakly-matched groups to signal constellations

A signal constellation which has been subdivided by cosets into subconstellations may not be geometrically uniform (i.e. not all cosets have the same list of distances to other cosets). The geometrically uniform cases have an isomorphic mapping between an algebraic group and the minimum coset distances of the constellation. The nongeometrically uniform constellations may have an algebraic group which matches the weakest list of coset distances. Otherwise, there may be a group which matches a lower-bound list of distances. TCM codes can be designed over these weakly-matched groups, or lower-bound-matched groups, and will have codeword-independent lower-bound distance properties