  The present paper is devoted to the study of the combinatorics of 216 maximal
$C^3$ circular codes --- a particular type of structure arising in the analysis
of genomic sequences. Their circularity property is believed to be intimately
connected to the protection against the reading frame shift in the process of
RNA translation. We present some new observations concerning the internal
structure of circular codes, which give a way to construct all of them in a
relatively simple manner.
