We develop ideas on genome replication introduced in Battail [Europhys. Lett. 40 (1997) 343]. Starting with the hypothesis that the genome replication process uses error-correcting means, and the auxiliary one that nested codes are used to this end, we first review the concepts of redundancy and error-correcting codes. Then we show that these hypotheses imply that: distinct species exist with a hierarchical taxonomy, there is a trend of evolution towards complexity, and evolution proceeds by discrete jumps. At least the first two features above may be considered as biological facts so, in the absence of direct evidence, they provide an indirect proof in favour of the hypothesized error-correction system. The very high redundancy of genomes makes it possible. In order to explain how it is implemented, we suggest that soft codes and replication decoding, to be briefly described, are plausible candidates. Experimentally proven properties of long-range correlation of the DNA message substantiate this claim.