It has been proposed that the degeneracy of the genetic code,i.e., the
phenomenon that different codons (base triplets) of DNA are transcribed into
the same amino acid, may be interpreted as the result of a symmetry breaking
process. In the initial work of Hornos & Hornos this picture was developed in
the framework of simple Lie algebras. Here, we explore the possibility of
explaining the degeneracy of the genetic code using basic classical Lie
superalgebras, whose representation theory is sufficiently well understood, at
least as far as typical representations are concerned. In the present paper, we
give the complete list of all typical codon representations (typical 64
-dimensional irreducible representations), whereas in the second part, we shall
present the corresponding branching rules and discuss which of them reproduce
the multiplet structure of the genetic code.