  Generalized quasi-cyclic (GQC) codes form a natural generalization of
quasi-cyclic (QC) codes. They are viewed here as mixed alphabet codes over a
family of ring alphabets. Decomposing these rings into local rings by the
Chinese Remainder Theorem yields a decomposition of GQC codes into a sum of
concatenated codes. This decomposition leads to a trace formula, a minimum
distance bound, and to a criteria for the GQC code to be self-dual or to be
linear complementary dual (LCD). Explicit long GQC codes that are LCD, but not
QC, are exhibited.
