Representing the Genetic Code as a Function on a Galois Field Using the Reed-Muller Expansion

Abstract

The information needed for the biotic activities of an organism is stored in a coded form in its DNA. This code is universal for all organisms and uses three units called nucleotides, each of which can take one of four possible values to code for twenty different amino acids. Thus it is a mapping from N3 toP, where N is the set of nucleotides and P is the set of Amino acids. The genetic code has been studied from the points of view of Coding Theory and Information Theory. Here we study it from the point of view of Switching Theory where it is considered as a logic function on a finite field and represented by its Reed-Muller expansion. We first present the genetic code, then develop its Reed-Muller expansion. Potential applications for this approach are also discussed.