Studying Genetic Code by a Matrix Approach

Abstract

Following Petoukhov and his collaborators, we use two length n zero-one sequences, α and β, to represent a length n genetic sequence ${\alpha\choose\beta}$ so that the columns of ${\alpha\choose\beta}$ have the following correspondence with the nucleotides: $C\sim{0\choose0}$ , $U\sim{1\choose0}$ , $G\sim{1\choose1}$ , $A\sim{0\choose1}$ . Using the Gray code ordering to arrange α and β, we build a 2ⁿ×2ⁿ matrix C _n including all the 4ⁿ length n genetic sequences. Furthermore, we use the Hamming distance of α and β to construct a 2ⁿ×2ⁿ matrix D _n . We explore structures of these matrices, refine the results in earlier papers, and propose new directions for further research.