We introduced nested search methods to design (n, k) block codes for arbitrary channels by optimizing an appropriate metric spectrum in each iteration. For a given k, the methods start with a good high rate code, say k/(k + 1), and successively design lower rate codes up to rate k/2^k corresponding to a Hadamard code. The design methodology was extended to the generic complex codes by utilizing columns of newly derived or existing unitary codes. Extensive comparisons to metric bounds and to previously designed codes show the optimality or near- optimality of the new codes. Further, the method was generalized such that good codes for arbitrary channels can be designed given the corresponding metric or the pairwise error probability. Finally, the introduction of the asymptotically optimum convolutional codes for a given constraint length, reduces dramatically the search size for good convolutional codes of a certain asymptotic performance, and the consequences to coded code- division multiple access (CDMA) system design are highlighted.
