The present invention presents an analysis for deoxyribose nucleic acid (DNA) and ribonucleic acid (RNA) standard genetic codes based on block circulant jacket matrix (BCJM) characteristics used to develop bioinformatics for molecular biology. The DNA matrix is decomposed in the form of a Kronecker product of a Hadamard matrix with an identity matrix and pair complementarity. A 16 × 4 Nirenberg RNA standard genetic code has asymmetric pair complementarity of a core kernel. A variant of a kernel of the Kronecker family is generated by a permutation of four characters with or without noise immunity. Accordingly, the present invention proposes the design of six subset patterns of block circulant matrices, six top-bottom block symmetry matrices, and six left-right block symmetry matrices. Degradation from DNA to RNA very clearly leads to noise immunity of the Kronecker product of symmetric gene matrices.
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