Genotype and phenotype are both the themes of modern biology.  Despite the elegant protein coding rules recognized decades ago in genotype, little is known on how traits are coded in a phenotype space (P).  Mathematically, P can be partitioned into a subspace determined by genetic factors (P^G) and a subspace affected by non-genetic factors (P^NG).  Evolutionary theory predicts P^G is composed of limited dimensions while P^NG may have infinite dimensions, which suggests a novel dimension decomposition method termed as uncorrelation-based high-dimensional dependence (UBHDD) to separate them.  We applied UBHDD to a yeast phenotype space comprising ~400 traits in ~1,000 individuals.  The obtained yeast P^G matches the actual genetic components of the yeast traits, explains the broad-sense heritability, and facilitates the mapping of quantitative trait loci, highlighting the success of the subspace separation.  A limited number of latent dimensions in the P^G were found to be recurrently used for coding the diverse yeast traits, while dimensions in the P^NG tend to be trait specific and increase constantly with trait sampling.  Similar results were obtained by applying UBHDD to the UK Biobank human brain phenome that comprises ~700 traits in ~26,000 individuals.  The results elucidated the genetic versus non-genetic origins of the left-right asymmetry of human brain, and enabled the discovery of a large number of novel genetic correlations between brain subregions and mental disorders.  In sum, phenotypic traits are coded by a limited number of genetically determined latent dimensions and unlimited trait-specific dimensions that are shaped by non-genetic factors, a rule fundamental to the emerging field of phenomics.