Linear codes and the mitochondrial genetic code

Abstract

The origin of the genetic code can certainly be regarded as one of the most challenging problems in the theory of molecular evolution. Thus the known variants of the genetic code and a possible common ancestry of them haven been studied extensively in the literature. Gonzalez et al. (2012) developed the theory of a primeval mitochondrial genetic code composed of four base codons. These were called tesserae and it was shown that the tesserae code has some remarkable error detection capabilities. In our paper we will show that using classical coding theory we can construct the tessera code as a linear coding of the standard genetic code and at the same time it can be deduced from the code of all dinucleotides by Plotkin's construction. It shows that the tessera model of the mitochondrial code does not just have a biological explanation but also has a clear mathematical structure. This underlines the role that the tessera model might have played in evolution.