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In this correspondence, we present a technique for generation of linear subcodes of a given turbo code with better distance spectrum than the original mother turbo code, via an iterative process of trace-bit injection which minimally reduces code rate, followed by selective puncturing that allows recovery of the rate loss incurred during the trace-bit injection. The technique allows for asymptotic performance improvement of any linear turbo code. In effect, we trim the distance spectrum of a turbo code via elimination of the low distance and/or high multiplicity codewords from the output space of the code. To this end, we perform a greedy minimization of a cost function closely related to the asymptotic bit error probability (or frame error probability) of the code. This improves the performance of the code everywhere, but its main impact is a reduction in the error floor of the turbo code which is important for delay constrained applications employing short interleavers.