On the Existence of $q$-ary Generalized Concatenated Codes with Optimal Error-Correcting Properties

We investigate the class of $q$-ary generalized concatenated codes with inner random block codes and outer nonrandom Reed–Solomon codes. We show that in memoryless $q$-ary symmetric discrete channels these codes asymptotically attain, for all transmission rates, the optimal error exponent of block codes.