It is a rather straightforward exercise to compute the DT code for a knot. My question is:
How does one produce the minimal such code?
For instance, I took this projection of $8_{19}$:
And arrived at the "best" code for this particular projection
[6 ... ]
(Note the signs are missing; this is from a screenshot.)
The latter projection gives the the minimal DT code.
How does one go about finding the minimal DT code? Searches on the internet commonly reference that Knot programs use them, but I have not found a reference that explicitly indicates how to produce it.
For instance, one DT code I worked out for $8_{19}$ was
[6 10 16 12 14 2 8 4]
Further, without looking it up in the Knot Atlas, how would I be able to ascertain that I could "do better?"